explain graphical presentation of data

Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

• Graphic Presentation of Data

Apart from diagrams, Graphic presentation is another way of the presentation of data and information. Usually, graphs are used to present time series and frequency distributions. In this article, we will look at the graphic presentation of data and information along with its merits, limitations , and types.

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Construction of a graph.

The graphic presentation of data and information offers a quick and simple way of understanding the features and drawing comparisons. Further, it is an effective analytical tool and a graph can help us in finding the mode, median, etc.

We can locate a point in a plane using two mutually perpendicular lines – the X-axis (the horizontal line) and the Y-axis (the vertical line). Their point of intersection is the Origin .

We can locate the position of a point in terms of its distance from both these axes. For example, if a point P is 3 units away from the Y-axis and 5 units away from the X-axis, then its location is as follows:

Browse more Topics under Descriptive Statistics

• Definition and Characteristics of Statistics
• Stages of Statistical Enquiry
• Importance and Functions of Statistics
• Nature of Statistics – Science or Art?
• Application of Statistics
• Law of Statistics and Distrust of Statistics
• Meaning and Types of Data
• Methods of Collecting Data
• Sample Investigation
• Classification of Data
• Tabulation of Data
• Frequency Distribution of Data
• Diagrammatic Presentation of Data
• Measures of Central Tendency
• Mean Median Mode
• Measures of Dispersion
• Standard Deviation
• Variance Analysis

Some points to remember:

• We measure the distance of the point from the Y-axis along the X-axis. Similarly, we measure the distance of the point from the X-axis along the Y-axis. Therefore, to measure 3 units from the Y-axis, we move 3 units along the X-axis and likewise for the other coordinate .
• We then draw perpendicular lines from these two points.
• The point where the perpendiculars intersect is the position of the point P.
• We denote it as follows (3,5) or (abscissa, ordinate). Together, they are the coordinates of the point P.
• The four parts of the plane are Quadrants.
• Also, we can plot different points for a different pair of values.

General Rules for Graphic Presentation of Data and Information

There are certain guidelines for an attractive and effective graphic presentation of data and information. These are as follows:

• Suitable Title – Ensure that you give a suitable title to the graph which clearly indicates the subject for which you are presenting it.
• Unit of Measurement – Clearly state the unit of measurement below the title.
• Suitable Scale – Choose a suitable scale so that you can represent the entire data in an accurate manner.
• Index – Include a brief index which explains the different colors and shades, lines and designs that you have used in the graph. Also, include a scale of interpretation for better understanding.
• Data Sources – Wherever possible, include the sources of information at the bottom of the graph.
• Keep it Simple – You should construct a graph which even a layman (without any exposure in the areas of statistics or mathematics) can understand.
• Neat – A graph is a visual aid for the presentation of data and information. Therefore, you must keep it neat and attractive. Choose the right size, right lettering, and appropriate lines, colors, dashes, etc.

Merits of a Graph

• The graph presents data in a manner which is easier to understand.
• It allows us to present statistical data in an attractive manner as compared to tables. Users can understand the main features, trends, and fluctuations of the data at a glance.
• A graph saves time.
• It allows the viewer to compare data relating to two different time-periods or regions.
• The viewer does not require prior knowledge of mathematics or statistics to understand a graph.
• We can use a graph to locate the mode, median, and mean values of the data.
• It is useful in forecasting, interpolation, and extrapolation of data.

Limitations of a Graph

• A graph lacks complete accuracy of facts.
• It depicts only a few selected characteristics of the data.
• We cannot use a graph in support of a statement.
• A graph is not a substitute for tables.
• Usually, laymen find it difficult to understand and interpret a graph.
• Typically, a graph shows the unreasonable tendency of the data and the actual values are not clear.

Types of Graphs

Graphs are of two types:

• Time Series graphs
• Frequency Distribution graphs

Time Series Graphs

A time series graph or a “ histogram ” is a graph which depicts the value of a variable over a different point of time. In a time series graph, time is the most important factor and the variable is related to time. It helps in the understanding and analysis of the changes in the variable at a different point of time. Many statisticians and businessmen use these graphs because they are easy to understand and also because they offer complex information in a simple manner.

Further, constructing a time series graph does not require a user with technical skills. Here are some major steps in the construction of a time series graph:

• Represent time on the X-axis and the value of the variable on the Y-axis.
• Start the Y-value with zero and devise a suitable scale which helps you present the whole data in the given space.
• Plot the values of the variable and join different point with a straight line.
• You can plot multiple variables through different lines.

You can use a line graph to summarize how two pieces of information are related and how they vary with each other.

• You can compare multiple continuous data-sets easily
• You can infer the interim data from the graph line

Disadvantages

• It is only used with continuous data.

Use of a false Base Line

Usually, in a graph, the vertical line starts from the Origin. However, in some cases, a false Base Line is used for a better representation of the data. There are two scenarios where you should use a false Base Line:

• To magnify the minor fluctuation in the time series data
• To economize the space

Net Balance Graph

If you have to show the net balance of income and expenditure or revenue and costs or imports and exports, etc., then you must use a net balance graph. You can use different colors or shades for positive and negative differences.

Frequency Distribution Graphs

Let’s look at the different types of frequency distribution graphs.

A histogram is a graph of a grouped frequency distribution. In a histogram, we plot the class intervals on the X-axis and their respective frequencies on the Y-axis. Further, we create a rectangle on each class interval with its height proportional to the frequency density of the class.

Frequency Polygon or Histograph

A frequency polygon or a Histograph is another way of representing a frequency distribution on a graph. You draw a frequency polygon by joining the midpoints of the upper widths of the adjacent rectangles of the histogram with straight lines.

Frequency Curve

When you join the verticals of a polygon using a smooth curve, then the resulting figure is a Frequency Curve. As the number of observations increase, we need to accommodate more classes. Therefore, the width of each class reduces. In such a scenario, the variable tends to become continuous and the frequency polygon starts taking the shape of a frequency curve.

Cumulative Frequency Curve or Ogive

A cumulative frequency curve or Ogive is the graphical representation of a cumulative frequency distribution. Since a cumulative frequency is either of a ‘less than’ or a ‘more than’ type, Ogives are of two types too – ‘less than ogive’ and ‘more than ogive’.

Scatter Diagram

A scatter diagram or a dot chart enables us to find the nature of the relationship between the variables. If the plotted points are scattered a lot, then the relationship between the two variables is lesser.

Solved Question

Q1. What are the general rules for the graphic presentation of data and information?

Answer: The general rules for the graphic presentation of data are:

• Use a suitable title
• Clearly specify the unit of measurement
• Ensure that you choose a suitable scale
• Provide an index specifying the colors, lines, and designs used in the graph
• If possible, provide the sources of information at the bottom of the graph
• Keep the graph simple and neat.

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Descriptive Statistics

• Nature of Statistics – Science or Art?

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Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

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Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

• Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
• Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
• Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

• Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
• Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
• Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
• Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
• Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

• Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
• Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
• Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
• Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

• Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
• Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
• Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
• Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

• Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
• Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
• Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
• Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

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FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

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Graphical summaries of data #

Many powerful approaches to data analysis communicate their findings via graphs. These are an important counterpart to data analysis approaches that communicate their findings via numbers or tabless.

Here we will illustrate some of the most common approaches for graphical data analysis. Throughout this discussion, it is important to remember that graphical data analysis methods are subject to the same principles as non-graphical methods. A graph can be either informative or misleading, just like any other type of statistical result. To understand whether a graph is informative, we should consider the following:

Every graph should provide insight into the specific research question that is the overall goal of the data analysis.

The graph is constructed using a sample of data, but the purpose of the graph is to learn about the population that the sample represents.

What statistical principal or concept is the graph based on?

What are the theoretical properties of any numerical summaries that are shown in the graph?

Almost every statistical graphic conveys a statistical concept that can be defined in a non-graphical manner. Graphs may show associations, location, dispersion, tails, conditioning, or almost any other statistical feature of the data or population. Graphs make it easier for the viewer to digest such information, but when interpreting a graph it is always important to keep in mind the specific statistical concept on which the graph is based.

Statistical graphics have an aesthetic dimension that is usually not evident when presenting findings through, say, tables. Our goal here is to focus on the content of graphs, not their aesthetic properties. Very crude graphs that have deep content are much more informative than beautiful graphs that convey only superficial content. In recent years, the field of infographics has grown rapidly. There is no sharp line dividing infographics from statistical graphs, however in general, the former tend to convey relatively simple insights in an aesthetically engaging way, while the latter aim to convey deeper and more subtle insight, with less focus on presentation.

Challenges and limitations of graphs #

One of the main challenges in statistical graphics is to fit the greatest amount of useful information into a single graph, while allowing the graph to remain interpretable. More complex graphs can suffer from overplotting , in which the plot elements are so crowded on the page that they fall on top of each other. This can limit the legibility of plots formed from large datasets unless a great deal of preliminary summarization of the data is performed.

Another challenge that arises in graphing complex datasets is that most graphs are two-dimensional, so that they can be viewed on a screen (or printed on paper). Some graphing techniques extend to three dimensions, but many datasets have a natural dimensionality that is much greater than 2 or 3. A few methods for graphing work around this, but require more effort from the person viewing the graph.

Boxplots are a graphical representation of the distribution of a single quantitative variable. A boxplot is based on a set of quantiles calculated using a sample of data. Below is an example of a single boxplot, drawn horizontally, showing the distribution of income values based on a sample of 100 individuals.

The “box” in a boxplot (shaded blue above) spans from the 25th to the 75th percentiles of the data, with an additional line drawn cross-wise through the box at the median. “Whiskers” extend from either end of the box, and are intended to cover the range of the data, excluding “outliers”.

The concept of an outlier is extremely problematic and no generically useful definition of outliers has been proposed. For the purpose of drawing a boxplot, the most common convention is to plot the upper (right-most) whisker at the 75th percentile plus 1.5 times the IQR, or to the greatest data value less than this quantity. Analogously, the lower (left-most) whisker is drawn at the 25th percentile minus 1.5 times the IQR, or to the least data value greater than this quantity. Finally, individual points sometimes called “fliers” are drawn corresponding to any value that falls outside the range spanned by the whiskers. A single box-plot, as above, is often drawn horizontally, but may also be drawn vertically.

There are many alternative ways of defining the locations of the whiskers in a boxplot. The approach described above is most common, and is chosen so that with “light tailed” distributions, well under 1% of the data will fall outside of of the whiskers.

The boxplot above shows a right-skewed distribution. This is evident because the upper whisker is further from the box than the lower whisker. Also, within the box, the median is closer to the lower side of the box than to the upper side of the box. Overall, the lower quantiles are more compressed, and the upper quantiles are more spread out, which is a feature of right-skewed distributions.

Side-by-side boxplots #

Boxplots are commonly used to compare distributions. A “side-by-side” or “grouped” boxplot is a collection of boxplots drawn for different subsets of data, plotted on the same axes. These subsets usually result from a stratification of the data, according to some stratifying factor that partially accounts for the heterogeneity within the population of interest. For example, below we consider boxplots showing the distribution of income, stratified by sex.

Histograms #

A histogram is a very familiar way to visualize quantitative data. A histogram is constructed by breaking the range of the values into bins and counting the number (or proportion) of observations that fall into each bin. The shape of a histogram shows visually how likely we are to observe data value in each part of the range. We are more likely to observe values where the histogram bars are higher, and less likely to observe values where the histogram bars are lower.

Histograms closely resemble “bar charts”, but with the added statistical aspect that the goal is to capture the density at each possible point in the population. “Density” is a measure of how commonly we observe data “near”, rather than “at” a point. For example, the density of household incomes at 45,000 USD would not be the exact number or frequency of households with this income. Instead, it reflects the frequency of households that have an income near 45,000 USD.

A histogram can be used to assess almost any property of a distribution. The common measures of location and dispersion can be judged from visual inspection of the histogram. As always, we should remember that features of the histogram may not always reflect features of the population from which the data were sampled. For example, a histogram may show two modes (i.e. is bimodal ) even when the underlying distribution only has one mode (i.e. is unimodal ). Moreover, the number of modes in a histogram can change as the bin width is varied.

Histograms are easy to communicate about, but may not be effective when working with small samples, where they can accentuate non-generalizable features of the sample (i.e. characteristics of the sample that are not present in the population). This is reflected in the following mathematical fact. For many statistics, if we wish to reduce the error relative to the population value of the statistic by a factor of two, we need to increase the sample size by a factor of four. In the case where we are aiming to estimate a density, in order to reduce the error by a factor of two, we need to increase the sample size by a factor of eight.

With a sufficiently large collection of representative data, the histogram should closely match the population’s probability density function (PDF). The PDF is usually a smooth curve, rather than a series of steps as in a histogram. This fact inspired the development of a modified version of a histogram that presents us with a smooth curve instead of a series of steps. This technique is called kernel density estimation ( KDE ). It produces graphs such as shown below.

Kernel density estimates may provide a somewhat more accurate estimation of the underlying density function compared to a histogram. But like a histogram, they can be unstable and produce artifacts. For example, the KDE above shows positive density for negative income values, even though all of the income values used to fit the KDE were positive (in some cases, income can take a negative value, but in this case no such values were present). More advanced KDE methods not used here can mitigate this issue.

One advantage of using a KDE rather than a histogram is that it is easier to overlay multiple KDEs on the same axes for comparison without too much overplotting. This might allow us to compare, say, the distributions of female and male incomes as follows.

Quantile plots #

A quantile plot is a plot of the pairs \((p, q_p)\) , where \(q_p\) is the p’th quantile of a collection of quantitative values. Since \(p\) can be any real number between 0 and 1, the graph of these pairs constitutes a function. By construction, this must be a non-decreasing function. A quantile plot contains essentially the same information as a histogram, but is represented in a very different way. Note that unlike the histogram, for which the bin width is a parameter that must be selected, there is no such parameter in the quantile plot. Arguably, the quantile plot is a more stable and informative summary of a sample, especially if the sample size is moderate. However most people are more comfortable interpreting histograms than quantile functions.

As an example, the following plot shows simulated systolic blood pressure values for a sample of females and a sample of males. In this case, at every probability point \(p\) , the blood pressure quantile for males is greater than the blood pressure quantile for females, indicating that male blood pressure is “stochastically greater” than female blood pressure.

Below is another example that shows two quantile functions, but in this case the quantile functions cross. As a result, there is no “stochastic ordering” between the data for females and for males. Also note that the quantile curve for females is steeper than the curve for males, indicating that the female blood pressure values are more dispersed than those for the males.

Quantile-quantile plots #

A quantile-quantile plot , or QQ plot , is a plot based on quantiles that is used to compare two distributions. Recall that a quantile plot plots the pairs \((p, q_p)\) for one sample. A QQ plot plots the pairs \((q^{(1)}_p, q^{(2)}_p)\) , where \(q^{(1)}_p\) are the quantiles for the first sample, and \(q^{(2)}_p\) are the quantiles for the second sample. In a QQ-plot, the value of p is “implicit” – each point on the graph corresponds to a specific value of p, but you cannot see what this value is by inspecting the graph.

As an example, suppose we are comparing the number of minutes of sleep during one night for teenagers and adults. This might give us the following QQ-plot:

The above QQ-plot shows us that teenagers tend to sleep longer than adults, and this is especially true at the upper end of the range. The QQ-plot approximately passes through the point (600, 800), meaning that for some probability p, 600 is the p’th quantile for adults and 800 is the p’th quantile for teenagers.

The slope of the curve in the QQ-plot reflects the relative levels of dispersion in the two distributions being compared. Since the slope of the curve in the above QQ-plot is greater than that of the diagonal reference line, it follows that the values plotted on the vertical axis (teenager’s values) are more dispersed than the values plotted on the horizontal axis (adult’s values).

An important property of a QQ-plot is that if the plot shows a linear relationship between the quantiles, then the two distributions are related via a location/scale transformation . That is, there is a linear function \(a + bx\) that maps one distribution to the other. In the example above, there is a substantial amount of curvature in the graph, so it does not seem to be the case that the sleep durations for adults and teenagers are related via a location/scale transformation.

Dot plots #

Dot plots display quantitative data that are stratified into groups. One axis of the plot is used to display the quantitative measure, and the other axis is used to separate the results for different groups. A series of parallel “guide lines” are used to show which points belong to each group. Dot plots are often used to display a collection of numerical summary statistics in visual form. Sometimes people say that dot plots are used to “convert tables into graphs”. Due to overplotting, dot plots are less commonly used to show raw data. The example below shows how dot plots can be used to display the median age stratified by sex, for people living in each of eleven countries.

The plot above shows that the median age for females is greater than the median age for males in every country. This is mainly due to females having longer life expectancies than males. We also see that some countries have much lower median ages for both sexes compared to other countries. Countries that have recently had high birth rates, such as Ethiopia and Nigeria, tend to have much lower median ages than countries with lower birth rates, such as Japan.

Scatterplots #

A scatterplot is a very widely-used method for visualizing bivariate data. They have many uses, but the most relevant for us is to plot the joint (empirical) distribution of two quantitative values. As an example, suppose that we observe paired data values giving the annual minimum and annual maximum temperature at a location. We could view these data with a scatterplot, placing, say, the minimum temperature value on the horizontal (x) axis, and the maximum temperature value on the vertical (y) axis. The number of points is the sample size, here being the number of locations for which temperature data are available. A possible graph of this type is shown below.

Several characteristics of the relationship between minimum and maximum temperature are evident from the plot above. The maximum temperature at each location is at least as large as the minimum temperature. There is a positive association in which locations with a lower minimum temperature tend to have a lower maximum temperature compared to places with a higher maximum temperature, but there is a lot of scatter around this trend. Warmer places tend to have a smaller range between their minimum and maximum temperatures. Concretely, locations on the equator and at low elevation, such as Singapore, have relatively constant temperature throughout the year. Locations near the center of large continents, like Winnipeg, Canada, can have extremely cold winters and also rather hot summers. Coastal regions that are far from the equator, such as Dublin, Ireland, have mild winters and cool summers.

To aid in interpreting a scatterplot, it is useful to plot a smooth curve that runs through the center of the data. This is called scatterplot smoothing , and can be accomplished with several algorithms, one of which is known as lowess . The population analogue of a scatterplot smooth is the conditional mean , or conditional expectation , denoted \(E[Y|X=x]\) , for the conditional mean of \(Y\) given \(X\) . The conditional mean is a function of \(x\) , and can be evaluated at any point \(x\) in the domain of \(X\) . The conditional mean is (roughly speaking), the average of all values of \(Y\) whose corresponding value of \(X\) is near \(x\) .

The plot below adds the estimated conditional mean (orange curve) to the scatterplot of temperature data discussed above. The conditional mean curve is increasing, showing that, as noted above, a location with lower annual minimum temperature tends on average to have a lower annual maximum temperature (relative to other locations).

Time series plots #

Some data have a serial structure, meaning that the values are observed with an ordering. Very often, such observations are made over time, which gives us time series or longitudinal data. Sometimes we observe a single time series over a long period of time, such as the value of a commodity in a market recorded every day over many years. Other times, we observe many short time series recorded irregularly. We may plot these time series together, leading to what is sometimes called a “spaghetti plot”. For example, in a study of human growth, we may observe measurements of the body weight of research subjects at various ages, giving us the spaghetti plot below:

Parallel coordinate plots #

Scatterplots in the plane are limited to two dimensions. Various techniques have been developed to overcome this limitation, one of which is the parallel coordinate plot . A parallel coordinate plot places the coordinate axes for the multiple dimensions as parallel lines, rather than as perpendicular lines. Using parallel lines means that data for far more than two or three variables can be placed on a single page.

Below is an example of a parallel coordinates plot, showing four attributes of a set of ten countries. A scatterplot of these points would live in four-dimensional space, which is quite challenging to visualize directly. Note that the attributes are converted to Z-scores, which is common in a parallel coordinates plot when the variables being plotted fall in very different ranges. The plot shows us that the life expectancies for females and for males are quite similar – the country with the highest life expectancy for females also has the highest life expectancy for males, and the country with the lowest life expectancy for females also has the lowest life expectancy for males. There is also a substantial positive relationship between the economic status of a country, as measured by its gross domestic product (GDP) and life expectancy. However no relationship is evident between GDP and population, or between either of the life expectancy variables and population.

Mosaic plots #

The graphs above primarily use quantitative data. A mosaic plot is a plot that is used with nominal data. Specifically mosaic plots are used when the units of analysis are cross-classified according to two nominal factors. In the example below, people with cancer are cross-classified by their biological sex, and by the type of cancer that they have:

The width of each box in the mosaic plot corresponds to the relative overall prevalence of the corresponding cancer type. The heights of the boxes correspond to the sex-specific prevalences. Based on this graph, we see that digestive, lung, and breast cancers are much more common than, say, oral and endocrine cancers. The mosaic plot also shows us that while breast and endocrine cancers are more common in females, the other cancer types are more common in males.

An important property of a mosaic plot is that the area of each box is proportional to the number of units that fall into the box. Thus, we can see that the area of the female breast cancer box is larger than the the combined areas of the female and male lung cancer boxes. Thus, there are more cases of breast cancer in females than the combined cases of lung cancer for both sexes.

Home Blog Design Understanding Data Presentations (Guide + Examples)

Understanding Data Presentations (Guide + Examples)

In this age of overwhelming information, the skill to effectively convey data has become extremely valuable. Initiating a discussion on data presentation types involves thoughtful consideration of the nature of your data and the message you aim to convey. Different types of visualizations serve distinct purposes. Whether you’re dealing with how to develop a report or simply trying to communicate complex information, how you present data influences how well your audience understands and engages with it. This extensive guide leads you through the different ways of data presentation.

Table of Contents

What is a Data Presentation?

What should a data presentation include, line graphs, treemap chart, scatter plot, how to choose a data presentation type, recommended data presentation templates, common mistakes done in data presentation.

A data presentation is a slide deck that aims to disclose quantitative information to an audience through the use of visual formats and narrative techniques derived from data analysis, making complex data understandable and actionable. This process requires a series of tools, such as charts, graphs, tables, infographics, dashboards, and so on, supported by concise textual explanations to improve understanding and boost retention rate.

Data presentations require us to cull data in a format that allows the presenter to highlight trends, patterns, and insights so that the audience can act upon the shared information. In a few words, the goal of data presentations is to enable viewers to grasp complicated concepts or trends quickly, facilitating informed decision-making or deeper analysis.

Data presentations go beyond the mere usage of graphical elements. Seasoned presenters encompass visuals with the art of storytelling with data, so the speech skillfully connects the points through a narrative that resonates with the audience. Depending on the purpose – inspire, persuade, inform, support decision-making processes, etc. – is the data presentation format that is better suited to help us in this journey.

To nail your upcoming data presentation, ensure to count with the following elements:

• Clear Objectives: Understand the intent of your presentation before selecting the graphical layout and metaphors to make content easier to grasp.
• Engaging introduction: Use a powerful hook from the get-go. For instance, you can ask a big question or present a problem that your data will answer. Take a look at our guide on how to start a presentation for tips & insights.
• Structured Narrative: Your data presentation must tell a coherent story. This means a beginning where you present the context, a middle section in which you present the data, and an ending that uses a call-to-action. Check our guide on presentation structure for further information.
• Visual Elements: These are the charts, graphs, and other elements of visual communication we ought to use to present data. This article will cover one by one the different types of data representation methods we can use, and provide further guidance on choosing between them.
• Insights and Analysis: This is not just showcasing a graph and letting people get an idea about it. A proper data presentation includes the interpretation of that data, the reason why it’s included, and why it matters to your research.
• Conclusion & CTA: Ending your presentation with a call to action is necessary. Whether you intend to wow your audience into acquiring your services, inspire them to change the world, or whatever the purpose of your presentation, there must be a stage in which you convey all that you shared and show the path to staying in touch. Plan ahead whether you want to use a thank-you slide, a video presentation, or which method is apt and tailored to the kind of presentation you deliver.
• Q&A Session: After your speech is concluded, allocate 3-5 minutes for the audience to raise any questions about the information you disclosed. This is an extra chance to establish your authority on the topic. Check our guide on questions and answer sessions in presentations here.

Bar charts are a graphical representation of data using rectangular bars to show quantities or frequencies in an established category. They make it easy for readers to spot patterns or trends. Bar charts can be horizontal or vertical, although the vertical format is commonly known as a column chart. They display categorical, discrete, or continuous variables grouped in class intervals [1] . They include an axis and a set of labeled bars horizontally or vertically. These bars represent the frequencies of variable values or the values themselves. Numbers on the y-axis of a vertical bar chart or the x-axis of a horizontal bar chart are called the scale.

Real-Life Application of Bar Charts

Let’s say a sales manager is presenting sales to their audience. Using a bar chart, he follows these steps.

Step 1: Selecting Data

The first step is to identify the specific data you will present to your audience.

The sales manager has highlighted these products for the presentation.

• Product A: Men’s Shoes
• Product B: Women’s Apparel
• Product C: Electronics
• Product D: Home Decor

Step 2: Choosing Orientation

Opt for a vertical layout for simplicity. Vertical bar charts help compare different categories in case there are not too many categories [1] . They can also help show different trends. A vertical bar chart is used where each bar represents one of the four chosen products. After plotting the data, it is seen that the height of each bar directly represents the sales performance of the respective product.

It is visible that the tallest bar (Electronics – Product C) is showing the highest sales. However, the shorter bars (Women’s Apparel – Product B and Home Decor – Product D) need attention. It indicates areas that require further analysis or strategies for improvement.

Step 3: Colorful Insights

Different colors are used to differentiate each product. It is essential to show a color-coded chart where the audience can distinguish between products.

• Men’s Shoes (Product A): Yellow
• Women’s Apparel (Product B): Orange
• Electronics (Product C): Violet
• Home Decor (Product D): Blue

Bar charts are straightforward and easily understandable for presenting data. They are versatile when comparing products or any categorical data [2] . Bar charts adapt seamlessly to retail scenarios. Despite that, bar charts have a few shortcomings. They cannot illustrate data trends over time. Besides, overloading the chart with numerous products can lead to visual clutter, diminishing its effectiveness.

For more information, check our collection of bar chart templates for PowerPoint .

Line graphs help illustrate data trends, progressions, or fluctuations by connecting a series of data points called ‘markers’ with straight line segments. This provides a straightforward representation of how values change [5] . Their versatility makes them invaluable for scenarios requiring a visual understanding of continuous data. In addition, line graphs are also useful for comparing multiple datasets over the same timeline. Using multiple line graphs allows us to compare more than one data set. They simplify complex information so the audience can quickly grasp the ups and downs of values. From tracking stock prices to analyzing experimental results, you can use line graphs to show how data changes over a continuous timeline. They show trends with simplicity and clarity.

Real-life Application of Line Graphs

To understand line graphs thoroughly, we will use a real case. Imagine you’re a financial analyst presenting a tech company’s monthly sales for a licensed product over the past year. Investors want insights into sales behavior by month, how market trends may have influenced sales performance and reception to the new pricing strategy. To present data via a line graph, you will complete these steps.

First, you need to gather the data. In this case, your data will be the sales numbers. For example:

• January: $45,000
• February: $55,000
• March: $45,000
• April: $60,000
• May: $ 70,000
• June: $65,000
• July: $62,000
• August: $68,000
• September: $81,000
• October: $76,000
• November: $87,000
• December: $91,000

After choosing the data, the next step is to select the orientation. Like bar charts, you can use vertical or horizontal line graphs. However, we want to keep this simple, so we will keep the timeline (x-axis) horizontal while the sales numbers (y-axis) vertical.

Step 3: Connecting Trends

After adding the data to your preferred software, you will plot a line graph. In the graph, each month’s sales are represented by data points connected by a line.

Step 4: Adding Clarity with Color

If there are multiple lines, you can also add colors to highlight each one, making it easier to follow.

Line graphs excel at visually presenting trends over time. These presentation aids identify patterns, like upward or downward trends. However, too many data points can clutter the graph, making it harder to interpret. Line graphs work best with continuous data but are not suitable for categories.

For more information, check our collection of line chart templates for PowerPoint and our article about how to make a presentation graph .

A data dashboard is a visual tool for analyzing information. Different graphs, charts, and tables are consolidated in a layout to showcase the information required to achieve one or more objectives. Dashboards help quickly see Key Performance Indicators (KPIs). You don’t make new visuals in the dashboard; instead, you use it to display visuals you’ve already made in worksheets [3] .

Keeping the number of visuals on a dashboard to three or four is recommended. Adding too many can make it hard to see the main points [4]. Dashboards can be used for business analytics to analyze sales, revenue, and marketing metrics at a time. They are also used in the manufacturing industry, as they allow users to grasp the entire production scenario at the moment while tracking the core KPIs for each line.

Real-Life Application of a Dashboard

Consider a project manager presenting a software development project’s progress to a tech company’s leadership team. He follows the following steps.

Step 1: Defining Key Metrics

To effectively communicate the project’s status, identify key metrics such as completion status, budget, and bug resolution rates. Then, choose measurable metrics aligned with project objectives.

Step 2: Choosing Visualization Widgets

After finalizing the data, presentation aids that align with each metric are selected. For this project, the project manager chooses a progress bar for the completion status and uses bar charts for budget allocation. Likewise, he implements line charts for bug resolution rates.

Step 3: Dashboard Layout

Key metrics are prominently placed in the dashboard for easy visibility, and the manager ensures that it appears clean and organized.

Dashboards provide a comprehensive view of key project metrics. Users can interact with data, customize views, and drill down for detailed analysis. However, creating an effective dashboard requires careful planning to avoid clutter. Besides, dashboards rely on the availability and accuracy of underlying data sources.

For more information, check our article on how to design a dashboard presentation , and discover our collection of dashboard PowerPoint templates .

Treemap charts represent hierarchical data structured in a series of nested rectangles [6] . As each branch of the ‘tree’ is given a rectangle, smaller tiles can be seen representing sub-branches, meaning elements on a lower hierarchical level than the parent rectangle. Each one of those rectangular nodes is built by representing an area proportional to the specified data dimension.

Treemaps are useful for visualizing large datasets in compact space. It is easy to identify patterns, such as which categories are dominant. Common applications of the treemap chart are seen in the IT industry, such as resource allocation, disk space management, website analytics, etc. Also, they can be used in multiple industries like healthcare data analysis, market share across different product categories, or even in finance to visualize portfolios.

Real-Life Application of a Treemap Chart

Let’s consider a financial scenario where a financial team wants to represent the budget allocation of a company. There is a hierarchy in the process, so it is helpful to use a treemap chart. In the chart, the top-level rectangle could represent the total budget, and it would be subdivided into smaller rectangles, each denoting a specific department. Further subdivisions within these smaller rectangles might represent individual projects or cost categories.

Step 1: Define Your Data Hierarchy

While presenting data on the budget allocation, start by outlining the hierarchical structure. The sequence will be like the overall budget at the top, followed by departments, projects within each department, and finally, individual cost categories for each project.

• Top-level rectangle: Total Budget
• Second-level rectangles: Departments (Engineering, Marketing, Sales)
• Third-level rectangles: Projects within each department
• Fourth-level rectangles: Cost categories for each project (Personnel, Marketing Expenses, Equipment)

Step 2: Choose a Suitable Tool

It’s time to select a data visualization tool supporting Treemaps. Popular choices include Tableau, Microsoft Power BI, PowerPoint, or even coding with libraries like D3.js. It is vital to ensure that the chosen tool provides customization options for colors, labels, and hierarchical structures.

Here, the team uses PowerPoint for this guide because of its user-friendly interface and robust Treemap capabilities.

Step 3: Make a Treemap Chart with PowerPoint

After opening the PowerPoint presentation, they chose “SmartArt” to form the chart. The SmartArt Graphic window has a “Hierarchy” category on the left.  Here, you will see multiple options. You can choose any layout that resembles a Treemap. The “Table Hierarchy” or “Organization Chart” options can be adapted. The team selects the Table Hierarchy as it looks close to a Treemap.

Step 5: Input Your Data

After that, a new window will open with a basic structure. They add the data one by one by clicking on the text boxes. They start with the top-level rectangle, representing the total budget.  

Step 6: Customize the Treemap

By clicking on each shape, they customize its color, size, and label. At the same time, they can adjust the font size, style, and color of labels by using the options in the “Format” tab in PowerPoint. Using different colors for each level enhances the visual difference.

Treemaps excel at illustrating hierarchical structures. These charts make it easy to understand relationships and dependencies. They efficiently use space, compactly displaying a large amount of data, reducing the need for excessive scrolling or navigation. Additionally, using colors enhances the understanding of data by representing different variables or categories.

In some cases, treemaps might become complex, especially with deep hierarchies.  It becomes challenging for some users to interpret the chart. At the same time, displaying detailed information within each rectangle might be constrained by space. It potentially limits the amount of data that can be shown clearly. Without proper labeling and color coding, there’s a risk of misinterpretation.

A heatmap is a data visualization tool that uses color coding to represent values across a two-dimensional surface. In these, colors replace numbers to indicate the magnitude of each cell. This color-shaded matrix display is valuable for summarizing and understanding data sets with a glance [7] . The intensity of the color corresponds to the value it represents, making it easy to identify patterns, trends, and variations in the data.

As a tool, heatmaps help businesses analyze website interactions, revealing user behavior patterns and preferences to enhance overall user experience. In addition, companies use heatmaps to assess content engagement, identifying popular sections and areas of improvement for more effective communication. They excel at highlighting patterns and trends in large datasets, making it easy to identify areas of interest.

We can implement heatmaps to express multiple data types, such as numerical values, percentages, or even categorical data. Heatmaps help us easily spot areas with lots of activity, making them helpful in figuring out clusters [8] . When making these maps, it is important to pick colors carefully. The colors need to show the differences between groups or levels of something. And it is good to use colors that people with colorblindness can easily see.

Check our detailed guide on how to create a heatmap here. Also discover our collection of heatmap PowerPoint templates .

Pie charts are circular statistical graphics divided into slices to illustrate numerical proportions. Each slice represents a proportionate part of the whole, making it easy to visualize the contribution of each component to the total.

The size of the pie charts is influenced by the value of data points within each pie. The total of all data points in a pie determines its size. The pie with the highest data points appears as the largest, whereas the others are proportionally smaller. However, you can present all pies of the same size if proportional representation is not required [9] . Sometimes, pie charts are difficult to read, or additional information is required. A variation of this tool can be used instead, known as the donut chart , which has the same structure but a blank center, creating a ring shape. Presenters can add extra information, and the ring shape helps to declutter the graph.

Pie charts are used in business to show percentage distribution, compare relative sizes of categories, or present straightforward data sets where visualizing ratios is essential.

Real-Life Application of Pie Charts

Consider a scenario where you want to represent the distribution of the data. Each slice of the pie chart would represent a different category, and the size of each slice would indicate the percentage of the total portion allocated to that category.

Step 1: Define Your Data Structure

Imagine you are presenting the distribution of a project budget among different expense categories.

• Column A: Expense Categories (Personnel, Equipment, Marketing, Miscellaneous)
• Column B: Budget Amounts ($40,000, $30,000, $20,000, $10,000) Column B represents the values of your categories in Column A.

Step 2: Insert a Pie Chart

Using any of the accessible tools, you can create a pie chart. The most convenient tools for forming a pie chart in a presentation are presentation tools such as PowerPoint or Google Slides.  You will notice that the pie chart assigns each expense category a percentage of the total budget by dividing it by the total budget.

For instance:

• Personnel: $40,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 40%
• Equipment: $30,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 30%
• Marketing: $20,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 20%
• Miscellaneous: $10,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 10%

You can make a chart out of this or just pull out the pie chart from the data.

3D pie charts and 3D donut charts are quite popular among the audience. They stand out as visual elements in any presentation slide, so let’s take a look at how our pie chart example would look in 3D pie chart format.

Step 03: Results Interpretation

The pie chart visually illustrates the distribution of the project budget among different expense categories. Personnel constitutes the largest portion at 40%, followed by equipment at 30%, marketing at 20%, and miscellaneous at 10%. This breakdown provides a clear overview of where the project funds are allocated, which helps in informed decision-making and resource management. It is evident that personnel are a significant investment, emphasizing their importance in the overall project budget.

Pie charts provide a straightforward way to represent proportions and percentages. They are easy to understand, even for individuals with limited data analysis experience. These charts work well for small datasets with a limited number of categories.

However, a pie chart can become cluttered and less effective in situations with many categories. Accurate interpretation may be challenging, especially when dealing with slight differences in slice sizes. In addition, these charts are static and do not effectively convey trends over time.

For more information, check our collection of pie chart templates for PowerPoint .

Histograms present the distribution of numerical variables. Unlike a bar chart that records each unique response separately, histograms organize numeric responses into bins and show the frequency of reactions within each bin [10] . The x-axis of a histogram shows the range of values for a numeric variable. At the same time, the y-axis indicates the relative frequencies (percentage of the total counts) for that range of values.

Whenever you want to understand the distribution of your data, check which values are more common, or identify outliers, histograms are your go-to. Think of them as a spotlight on the story your data is telling. A histogram can provide a quick and insightful overview if you’re curious about exam scores, sales figures, or any numerical data distribution.

Real-Life Application of a Histogram

In the histogram data analysis presentation example, imagine an instructor analyzing a class’s grades to identify the most common score range. A histogram could effectively display the distribution. It will show whether most students scored in the average range or if there are significant outliers.

Step 1: Gather Data

He begins by gathering the data. The scores of each student in class are gathered to analyze exam scores.

After arranging the scores in ascending order, bin ranges are set.

Step 2: Define Bins

Bins are like categories that group similar values. Think of them as buckets that organize your data. The presenter decides how wide each bin should be based on the range of the values. For instance, the instructor sets the bin ranges based on score intervals: 60-69, 70-79, 80-89, and 90-100.

Step 3: Count Frequency

Now, he counts how many data points fall into each bin. This step is crucial because it tells you how often specific ranges of values occur. The result is the frequency distribution, showing the occurrences of each group.

Here, the instructor counts the number of students in each category.

• 60-69: 1 student (Kate)
• 70-79: 4 students (David, Emma, Grace, Jack)
• 80-89: 7 students (Alice, Bob, Frank, Isabel, Liam, Mia, Noah)
• 90-100: 3 students (Clara, Henry, Olivia)

Step 4: Create the Histogram

It’s time to turn the data into a visual representation. Draw a bar for each bin on a graph. The width of the bar should correspond to the range of the bin, and the height should correspond to the frequency.  To make your histogram understandable, label the X and Y axes.

In this case, the X-axis should represent the bins (e.g., test score ranges), and the Y-axis represents the frequency.

The histogram of the class grades reveals insightful patterns in the distribution. Most students, with seven students, fall within the 80-89 score range. The histogram provides a clear visualization of the class’s performance. It showcases a concentration of grades in the upper-middle range with few outliers at both ends. This analysis helps in understanding the overall academic standing of the class. It also identifies the areas for potential improvement or recognition.

Thus, histograms provide a clear visual representation of data distribution. They are easy to interpret, even for those without a statistical background. They apply to various types of data, including continuous and discrete variables. One weak point is that histograms do not capture detailed patterns in students’ data, with seven compared to other visualization methods.

A scatter plot is a graphical representation of the relationship between two variables. It consists of individual data points on a two-dimensional plane. This plane plots one variable on the x-axis and the other on the y-axis. Each point represents a unique observation. It visualizes patterns, trends, or correlations between the two variables.

Scatter plots are also effective in revealing the strength and direction of relationships. They identify outliers and assess the overall distribution of data points. The points’ dispersion and clustering reflect the relationship’s nature, whether it is positive, negative, or lacks a discernible pattern. In business, scatter plots assess relationships between variables such as marketing cost and sales revenue. They help present data correlations and decision-making.

Real-Life Application of Scatter Plot

A group of scientists is conducting a study on the relationship between daily hours of screen time and sleep quality. After reviewing the data, they managed to create this table to help them build a scatter plot graph:

In the provided example, the x-axis represents Daily Hours of Screen Time, and the y-axis represents the Sleep Quality Rating.

The scientists observe a negative correlation between the amount of screen time and the quality of sleep. This is consistent with their hypothesis that blue light, especially before bedtime, has a significant impact on sleep quality and metabolic processes.

There are a few things to remember when using a scatter plot. Even when a scatter diagram indicates a relationship, it doesn’t mean one variable affects the other. A third factor can influence both variables. The more the plot resembles a straight line, the stronger the relationship is perceived [11] . If it suggests no ties, the observed pattern might be due to random fluctuations in data. When the scatter diagram depicts no correlation, whether the data might be stratified is worth considering.

Choosing the appropriate data presentation type is crucial when making a presentation . Understanding the nature of your data and the message you intend to convey will guide this selection process. For instance, when showcasing quantitative relationships, scatter plots become instrumental in revealing correlations between variables. If the focus is on emphasizing parts of a whole, pie charts offer a concise display of proportions. Histograms, on the other hand, prove valuable for illustrating distributions and frequency patterns. 

Bar charts provide a clear visual comparison of different categories. Likewise, line charts excel in showcasing trends over time, while tables are ideal for detailed data examination. Starting a presentation on data presentation types involves evaluating the specific information you want to communicate and selecting the format that aligns with your message. This ensures clarity and resonance with your audience from the beginning of your presentation.

1. Fact Sheet Dashboard for Data Presentation

Convey all the data you need to present in this one-pager format, an ideal solution tailored for users looking for presentation aids. Global maps, donut chats, column graphs, and text neatly arranged in a clean layout presented in light and dark themes.

Use This Template

2. 3D Column Chart Infographic PPT Template

Represent column charts in a highly visual 3D format with this PPT template. A creative way to present data, this template is entirely editable, and we can craft either a one-page infographic or a series of slides explaining what we intend to disclose point by point.

3. Data Circles Infographic PowerPoint Template

An alternative to the pie chart and donut chart diagrams, this template features a series of curved shapes with bubble callouts as ways of presenting data. Expand the information for each arch in the text placeholder areas.

4. Colorful Metrics Dashboard for Data Presentation

This versatile dashboard template helps us in the presentation of the data by offering several graphs and methods to convert numbers into graphics. Implement it for e-commerce projects, financial projections, project development, and more.

5. Animated Data Presentation Tools for PowerPoint & Google Slides

A slide deck filled with most of the tools mentioned in this article, from bar charts, column charts, treemap graphs, pie charts, histogram, etc. Animated effects make each slide look dynamic when sharing data with stakeholders.

6. Statistics Waffle Charts PPT Template for Data Presentations

This PPT template helps us how to present data beyond the typical pie chart representation. It is widely used for demographics, so it’s a great fit for marketing teams, data science professionals, HR personnel, and more.

7. Data Presentation Dashboard Template for Google Slides

A compendium of tools in dashboard format featuring line graphs, bar charts, column charts, and neatly arranged placeholder text areas. 

8. Weather Dashboard for Data Presentation

Share weather data for agricultural presentation topics, environmental studies, or any kind of presentation that requires a highly visual layout for weather forecasting on a single day. Two color themes are available.

9. Social Media Marketing Dashboard Data Presentation Template

Intended for marketing professionals, this dashboard template for data presentation is a tool for presenting data analytics from social media channels. Two slide layouts featuring line graphs and column charts.

10. Project Management Summary Dashboard Template

A tool crafted for project managers to deliver highly visual reports on a project’s completion, the profits it delivered for the company, and expenses/time required to execute it. 4 different color layouts are available.

11. Profit & Loss Dashboard for PowerPoint and Google Slides

A must-have for finance professionals. This typical profit & loss dashboard includes progress bars, donut charts, column charts, line graphs, and everything that’s required to deliver a comprehensive report about a company’s financial situation.

Overwhelming visuals

One of the mistakes related to using data-presenting methods is including too much data or using overly complex visualizations. They can confuse the audience and dilute the key message.

Inappropriate chart types

Choosing the wrong type of chart for the data at hand can lead to misinterpretation. For example, using a pie chart for data that doesn’t represent parts of a whole is not right.

Lack of context

Failing to provide context or sufficient labeling can make it challenging for the audience to understand the significance of the presented data.

Inconsistency in design

Using inconsistent design elements and color schemes across different visualizations can create confusion and visual disarray.

Failure to provide details

Simply presenting raw data without offering clear insights or takeaways can leave the audience without a meaningful conclusion.

Lack of focus

Not having a clear focus on the key message or main takeaway can result in a presentation that lacks a central theme.

Visual accessibility issues

Overlooking the visual accessibility of charts and graphs can exclude certain audience members who may have difficulty interpreting visual information.

In order to avoid these mistakes in data presentation, presenters can benefit from using presentation templates . These templates provide a structured framework. They ensure consistency, clarity, and an aesthetically pleasing design, enhancing data communication’s overall impact.

Understanding and choosing data presentation types are pivotal in effective communication. Each method serves a unique purpose, so selecting the appropriate one depends on the nature of the data and the message to be conveyed. The diverse array of presentation types offers versatility in visually representing information, from bar charts showing values to pie charts illustrating proportions. 

Using the proper method enhances clarity, engages the audience, and ensures that data sets are not just presented but comprehensively understood. By appreciating the strengths and limitations of different presentation types, communicators can tailor their approach to convey information accurately, developing a deeper connection between data and audience understanding.

[1] Government of Canada, S.C. (2021) 5 Data Visualization 5.2 Bar Chart , 5.2 Bar chart .  https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch9/bargraph-diagrammeabarres/5214818-eng.htm

[2] Kosslyn, S.M., 1989. Understanding charts and graphs. Applied cognitive psychology, 3(3), pp.185-225. https://apps.dtic.mil/sti/pdfs/ADA183409.pdf

[3] Creating a Dashboard . https://it.tufts.edu/book/export/html/1870

[4] https://www.goldenwestcollege.edu/research/data-and-more/data-dashboards/index.html

[5] https://www.mit.edu/course/21/21.guide/grf-line.htm

[6] Jadeja, M. and Shah, K., 2015, January. Tree-Map: A Visualization Tool for Large Data. In GSB@ SIGIR (pp. 9-13). https://ceur-ws.org/Vol-1393/gsb15proceedings.pdf#page=15

[7] Heat Maps and Quilt Plots. https://www.publichealth.columbia.edu/research/population-health-methods/heat-maps-and-quilt-plots

[8] EIU QGIS WORKSHOP. https://www.eiu.edu/qgisworkshop/heatmaps.php

[9] About Pie Charts.  https://www.mit.edu/~mbarker/formula1/f1help/11-ch-c8.htm

[10] Histograms. https://sites.utexas.edu/sos/guided/descriptive/numericaldd/descriptiven2/histogram/ [11] https://asq.org/quality-resources/scatter-diagram

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17 Data Visualization Techniques All Professionals Should Know

• 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

Access your free e-book today.

What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

• Gantt Chart
• Box and Whisker Plot
• Waterfall Chart
• Scatter Plot
• Pictogram Chart
• Highlight Table
• Bullet Graph
• Choropleth Map
• Network Diagram
• Correlation Matrices

1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

• Bubble clouds
• Circle views
• Dendrograms
• Dot distribution maps
• Open-high-low-close charts
• Polar areas
• Radial trees
• Ring Charts
• Sankey diagram
• Span charts
• Streamgraphs
• Wedge stack graphs
• Violin plots

Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

About the Author

Tapping the Power of PowerPoint for Medical Posters and Presentations pp 65–81 Cite as

Data Presentation: Use of Tables and Graphics

• Anand J. Thakur 2  
• First Online: 08 June 2022

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In an era of evidence based medicine, data is an important factor and needs to be presented in a way that is quickly understood by the audience. People are generally weak at understanding data. Visualization makes it easier for the audience to grasp and recall data. It should be presented in an attractive style to create interest in audience’s mind; Data may be presented as a table or graphic. There are 3 types of tables: Formal (numbers), textural, and matrix; each one has its peculiarities and usefulness. Rules for construction of these table are described. There are several graphics to present data and one that is most suitable for the variables under consideration is chosen. Numerical (quantitative) data is presented in a bar chart, pictogram, pie chart, or choropleth map. Descriptive, categorical, and frequency data (qualitative) are presented in histogram, frequency polygon, frequency curve, line chart, and scatter diagram. Decision trees and genealogical charts are used in special circumstances. Example of each of these graphics is discussed with its usefulness and shortcomings. Recommendations on use of tables and graphics for a specific data are made for expediency and usability.

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Thakur, A.J. (2022). Data Presentation: Use of Tables and Graphics. In: Tapping the Power of PowerPoint for Medical Posters and Presentations. Springer, Singapore. https://doi.org/10.1007/978-981-19-1816-2_8

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It is the simplest form of data Presentation often used in schools or universities to provide a clearer picture to students, who are better able to capture the concepts effectively through a pictorial Presentation of simple data.

2. Column chart

It is a simplified version of the pictorial Presentation which involves the management of a larger amount of data being shared during the presentations and providing suitable clarity to the insights of the data.

3. Pie Charts

Pie charts provide a very descriptive & a 2D depiction of the data pertaining to comparisons or resemblance of data in two separate fields.

4. Bar charts

A bar chart that shows the accumulation of data with cuboid bars with different dimensions & lengths which are directly proportionate to the values they represent. The bars can be placed either vertically or horizontally depending on the data being represented.

5. Histograms

It is a perfect Presentation of the spread of numerical data. The main differentiation that separates data graphs and histograms are the gaps in the data graphs.

6. Box plots

Box plot or Box-plot is a way of representing groups of numerical data through quartiles. Data Presentation is easier with this style of graph dealing with the extraction of data to the minutes of difference.

Map Data graphs help you with data Presentation over an area to display the areas of concern. Map graphs are useful to make an exact depiction of data over a vast case scenario.

All these visual presentations share a common goal of creating meaningful insights and a platform to understand and manage the data in relation to the growth and expansion of one’s in-depth understanding of data & details to plan or execute future decisions or actions.

Importance of Data Presentation

Data Presentation could be both can be a deal maker or deal breaker based on the delivery of the content in the context of visual depiction.

Data Presentation tools are powerful communication tools that can simplify the data by making it easily understandable & readable at the same time while attracting & keeping the interest of its readers and effectively showcase large amounts of complex data in a simplified manner.

If the user can create an insightful presentation of the data in hand with the same sets of facts and figures, then the results promise to be impressive.

There have been situations where the user has had a great amount of data and vision for expansion but the presentation drowned his/her vision.

To impress the higher management and top brass of a firm, effective presentation of data is needed.

Data Presentation helps the clients or the audience to not spend time grasping the concept and the future alternatives of the business and to convince them to invest in the company & turn it profitable both for the investors & the company.

Although data presentation has a lot to offer, the following are some of the major reason behind the essence of an effective presentation:-

• Many consumers or higher authorities are interested in the interpretation of data, not the raw data itself. Therefore, after the analysis of the data, users should represent the data with a visual aspect for better understanding and knowledge.
• The user should not overwhelm the audience with a number of slides of the presentation and inject an ample amount of texts as pictures that will speak for themselves.
• Data presentation often happens in a nutshell with each department showcasing their achievements towards company growth through a graph or a histogram.
• Providing a brief description would help the user to attain attention in a small amount of time while informing the audience about the context of the presentation
• The inclusion of pictures, charts, graphs and tables in the presentation help for better understanding the potential outcomes.
• An effective presentation would allow the organization to determine the difference with the fellow organization and acknowledge its flaws. Comparison of data would assist them in decision making.

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Statistical data presentation

1 Department of Anesthesiology and Pain Medicine, Dongguk University Ilsan Hospital, Goyang, Korea.

Sangseok Lee

2 Department of Anesthesiology and Pain Medicine, Sanggye Paik Hospital, Inje University College of Medicine, Seoul, Korea.

Data are usually collected in a raw format and thus the inherent information is difficult to understand. Therefore, raw data need to be summarized, processed, and analyzed. However, no matter how well manipulated, the information derived from the raw data should be presented in an effective format, otherwise, it would be a great loss for both authors and readers. In this article, the techniques of data and information presentation in textual, tabular, and graphical forms are introduced. Text is the principal method for explaining findings, outlining trends, and providing contextual information. A table is best suited for representing individual information and represents both quantitative and qualitative information. A graph is a very effective visual tool as it displays data at a glance, facilitates comparison, and can reveal trends and relationships within the data such as changes over time, frequency distribution, and correlation or relative share of a whole. Text, tables, and graphs for data and information presentation are very powerful communication tools. They can make an article easy to understand, attract and sustain the interest of readers, and efficiently present large amounts of complex information. Moreover, as journal editors and reviewers glance at these presentations before reading the whole article, their importance cannot be ignored.

Introduction

Data are a set of facts, and provide a partial picture of reality. Whether data are being collected with a certain purpose or collected data are being utilized, questions regarding what information the data are conveying, how the data can be used, and what must be done to include more useful information must constantly be kept in mind.

Since most data are available to researchers in a raw format, they must be summarized, organized, and analyzed to usefully derive information from them. Furthermore, each data set needs to be presented in a certain way depending on what it is used for. Planning how the data will be presented is essential before appropriately processing raw data.

First, a question for which an answer is desired must be clearly defined. The more detailed the question is, the more detailed and clearer the results are. A broad question results in vague answers and results that are hard to interpret. In other words, a well-defined question is crucial for the data to be well-understood later. Once a detailed question is ready, the raw data must be prepared before processing. These days, data are often summarized, organized, and analyzed with statistical packages or graphics software. Data must be prepared in such a way they are properly recognized by the program being used. The present study does not discuss this data preparation process, which involves creating a data frame, creating/changing rows and columns, changing the level of a factor, categorical variable, coding, dummy variables, variable transformation, data transformation, missing value, outlier treatment, and noise removal.

We describe the roles and appropriate use of text, tables, and graphs (graphs, plots, or charts), all of which are commonly used in reports, articles, posters, and presentations. Furthermore, we discuss the issues that must be addressed when presenting various kinds of information, and effective methods of presenting data, which are the end products of research, and of emphasizing specific information.

Data Presentation

Data can be presented in one of the three ways:

–as text;

–in tabular form; or

–in graphical form.

Methods of presentation must be determined according to the data format, the method of analysis to be used, and the information to be emphasized. Inappropriately presented data fail to clearly convey information to readers and reviewers. Even when the same information is being conveyed, different methods of presentation must be employed depending on what specific information is going to be emphasized. A method of presentation must be chosen after carefully weighing the advantages and disadvantages of different methods of presentation. For easy comparison of different methods of presentation, let us look at a table ( Table 1 ) and a line graph ( Fig. 1 ) that present the same information [ 1 ]. If one wishes to compare or introduce two values at a certain time point, it is appropriate to use text or the written language. However, a table is the most appropriate when all information requires equal attention, and it allows readers to selectively look at information of their own interest. Graphs allow readers to understand the overall trend in data, and intuitively understand the comparison results between two groups. One thing to always bear in mind regardless of what method is used, however, is the simplicity of presentation.

Values are expressed as mean ± SD. Group C: normal saline, Group D: dexmedetomidine. SBP: systolic blood pressure, DBP: diastolic blood pressure, MBP: mean blood pressure, HR: heart rate. * P < 0.05 indicates a significant increase in each group, compared with the baseline values. † P < 0.05 indicates a significant decrease noted in Group D, compared with the baseline values. ‡ P < 0.05 indicates a significant difference between the groups.

Text presentation

Text is the main method of conveying information as it is used to explain results and trends, and provide contextual information. Data are fundamentally presented in paragraphs or sentences. Text can be used to provide interpretation or emphasize certain data. If quantitative information to be conveyed consists of one or two numbers, it is more appropriate to use written language than tables or graphs. For instance, information about the incidence rates of delirium following anesthesia in 2016–2017 can be presented with the use of a few numbers: “The incidence rate of delirium following anesthesia was 11% in 2016 and 15% in 2017; no significant difference of incidence rates was found between the two years.” If this information were to be presented in a graph or a table, it would occupy an unnecessarily large space on the page, without enhancing the readers' understanding of the data. If more data are to be presented, or other information such as that regarding data trends are to be conveyed, a table or a graph would be more appropriate. By nature, data take longer to read when presented as texts and when the main text includes a long list of information, readers and reviewers may have difficulties in understanding the information.

Table presentation

Tables, which convey information that has been converted into words or numbers in rows and columns, have been used for nearly 2,000 years. Anyone with a sufficient level of literacy can easily understand the information presented in a table. Tables are the most appropriate for presenting individual information, and can present both quantitative and qualitative information. Examples of qualitative information are the level of sedation [ 2 ], statistical methods/functions [ 3 , 4 ], and intubation conditions [ 5 ].

The strength of tables is that they can accurately present information that cannot be presented with a graph. A number such as “132.145852” can be accurately expressed in a table. Another strength is that information with different units can be presented together. For instance, blood pressure, heart rate, number of drugs administered, and anesthesia time can be presented together in one table. Finally, tables are useful for summarizing and comparing quantitative information of different variables. However, the interpretation of information takes longer in tables than in graphs, and tables are not appropriate for studying data trends. Furthermore, since all data are of equal importance in a table, it is not easy to identify and selectively choose the information required.

For a general guideline for creating tables, refer to the journal submission requirements 1) .

Heat maps for better visualization of information than tables

Heat maps help to further visualize the information presented in a table by applying colors to the background of cells. By adjusting the colors or color saturation, information is conveyed in a more visible manner, and readers can quickly identify the information of interest ( Table 2 ). Software such as Excel (in Microsoft Office, Microsoft, WA, USA) have features that enable easy creation of heat maps through the options available on the “conditional formatting” menu.

All numbers were created by the author. SBP: systolic blood pressure, DBP: diastolic blood pressure, MBP: mean blood pressure, HR: heart rate.

Graph presentation

Whereas tables can be used for presenting all the information, graphs simplify complex information by using images and emphasizing data patterns or trends, and are useful for summarizing, explaining, or exploring quantitative data. While graphs are effective for presenting large amounts of data, they can be used in place of tables to present small sets of data. A graph format that best presents information must be chosen so that readers and reviewers can easily understand the information. In the following, we describe frequently used graph formats and the types of data that are appropriately presented with each format with examples.

Scatter plot

Scatter plots present data on the x - and y -axes and are used to investigate an association between two variables. A point represents each individual or object, and an association between two variables can be studied by analyzing patterns across multiple points. A regression line is added to a graph to determine whether the association between two variables can be explained or not. Fig. 2 illustrates correlations between pain scoring systems that are currently used (PSQ, Pain Sensitivity Questionnaire; PASS, Pain Anxiety Symptoms Scale; PCS, Pain Catastrophizing Scale) and Geop-Pain Questionnaire (GPQ) with the correlation coefficient, R, and regression line indicated on the scatter plot [ 6 ]. If multiple points exist at an identical location as in this example ( Fig. 2 ), the correlation level may not be clear. In this case, a correlation coefficient or regression line can be added to further elucidate the correlation.

Bar graph and histogram

A bar graph is used to indicate and compare values in a discrete category or group, and the frequency or other measurement parameters (i.e. mean). Depending on the number of categories, and the size or complexity of each category, bars may be created vertically or horizontally. The height (or length) of a bar represents the amount of information in a category. Bar graphs are flexible, and can be used in a grouped or subdivided bar format in cases of two or more data sets in each category. Fig. 3 is a representative example of a vertical bar graph, with the x -axis representing the length of recovery room stay and drug-treated group, and the y -axis representing the visual analog scale (VAS) score. The mean and standard deviation of the VAS scores are expressed as whiskers on the bars ( Fig. 3 ) [ 7 ].

By comparing the endpoints of bars, one can identify the largest and the smallest categories, and understand gradual differences between each category. It is advised to start the x - and y -axes from 0. Illustration of comparison results in the x - and y -axes that do not start from 0 can deceive readers' eyes and lead to overrepresentation of the results.

One form of vertical bar graph is the stacked vertical bar graph. A stack vertical bar graph is used to compare the sum of each category, and analyze parts of a category. While stacked vertical bar graphs are excellent from the aspect of visualization, they do not have a reference line, making comparison of parts of various categories challenging ( Fig. 4 ) [ 8 ].

A pie chart, which is used to represent nominal data (in other words, data classified in different categories), visually represents a distribution of categories. It is generally the most appropriate format for representing information grouped into a small number of categories. It is also used for data that have no other way of being represented aside from a table (i.e. frequency table). Fig. 5 illustrates the distribution of regular waste from operation rooms by their weight [ 8 ]. A pie chart is also commonly used to illustrate the number of votes each candidate won in an election.

Line plot with whiskers

A line plot is useful for representing time-series data such as monthly precipitation and yearly unemployment rates; in other words, it is used to study variables that are observed over time. Line graphs are especially useful for studying patterns and trends across data that include climatic influence, large changes or turning points, and are also appropriate for representing not only time-series data, but also data measured over the progression of a continuous variable such as distance. As can be seen in Fig. 1 , mean and standard deviation of systolic blood pressure are indicated for each time point, which enables readers to easily understand changes of systolic pressure over time [ 1 ]. If data are collected at a regular interval, values in between the measurements can be estimated. In a line graph, the x-axis represents the continuous variable, while the y-axis represents the scale and measurement values. It is also useful to represent multiple data sets on a single line graph to compare and analyze patterns across different data sets.

Box and whisker chart

A box and whisker chart does not make any assumptions about the underlying statistical distribution, and represents variations in samples of a population; therefore, it is appropriate for representing nonparametric data. AA box and whisker chart consists of boxes that represent interquartile range (one to three), the median and the mean of the data, and whiskers presented as lines outside of the boxes. Whiskers can be used to present the largest and smallest values in a set of data or only a part of the data (i.e. 95% of all the data). Data that are excluded from the data set are presented as individual points and are called outliers. The spacing at both ends of the box indicates dispersion in the data. The relative location of the median demonstrated within the box indicates skewness ( Fig. 6 ). The box and whisker chart provided as an example represents calculated volumes of an anesthetic, desflurane, consumed over the course of the observation period ( Fig. 7 ) [ 9 ].

Three-dimensional effects

Most of the recently introduced statistical packages and graphics software have the three-dimensional (3D) effect feature. The 3D effects can add depth and perspective to a graph. However, since they may make reading and interpreting data more difficult, they must only be used after careful consideration. The application of 3D effects on a pie chart makes distinguishing the size of each slice difficult. Even if slices are of similar sizes, slices farther from the front of the pie chart may appear smaller than the slices closer to the front ( Fig. 8 ).

Drawing a graph: example

Finally, we explain how to create a graph by using a line graph as an example ( Fig. 9 ). In Fig. 9 , the mean values of arterial pressure were randomly produced and assumed to have been measured on an hourly basis. In many graphs, the x- and y-axes meet at the zero point ( Fig. 9A ). In this case, information regarding the mean and standard deviation of mean arterial pressure measurements corresponding to t = 0 cannot be conveyed as the values overlap with the y-axis. The data can be clearly exposed by separating the zero point ( Fig. 9B ). In Fig. 9B , the mean and standard deviation of different groups overlap and cannot be clearly distinguished from each other. Separating the data sets and presenting standard deviations in a single direction prevents overlapping and, therefore, reduces the visual inconvenience. Doing so also reduces the excessive number of ticks on the y-axis, increasing the legibility of the graph ( Fig. 9C ). In the last graph, different shapes were used for the lines connecting different time points to further allow the data to be distinguished, and the y-axis was shortened to get rid of the unnecessary empty space present in the previous graphs ( Fig. 9D ). A graph can be made easier to interpret by assigning each group to a different color, changing the shape of a point, or including graphs of different formats [ 10 ]. The use of random settings for the scale in a graph may lead to inappropriate presentation or presentation of data that can deceive readers' eyes ( Fig. 10 ).

Owing to the lack of space, we could not discuss all types of graphs, but have focused on describing graphs that are frequently used in scholarly articles. We have summarized the commonly used types of graphs according to the method of data analysis in Table 3 . For general guidelines on graph designs, please refer to the journal submission requirements 2) .

Conclusions

Text, tables, and graphs are effective communication media that present and convey data and information. They aid readers in understanding the content of research, sustain their interest, and effectively present large quantities of complex information. As journal editors and reviewers will scan through these presentations before reading the entire text, their importance cannot be disregarded. For this reason, authors must pay as close attention to selecting appropriate methods of data presentation as when they were collecting data of good quality and analyzing them. In addition, having a well-established understanding of different methods of data presentation and their appropriate use will enable one to develop the ability to recognize and interpret inappropriately presented data or data presented in such a way that it deceives readers' eyes [ 11 ].

<Appendix>

Output for presentation.

Discovery and communication are the two objectives of data visualization. In the discovery phase, various types of graphs must be tried to understand the rough and overall information the data are conveying. The communication phase is focused on presenting the discovered information in a summarized form. During this phase, it is necessary to polish images including graphs, pictures, and videos, and consider the fact that the images may look different when printed than how appear on a computer screen. In this appendix, we discuss important concepts that one must be familiar with to print graphs appropriately.

The KJA asks that pictures and images meet the following requirement before submission 3)

“Figures and photographs should be submitted as ‘TIFF’ files. Submit files of figures and photographs separately from the text of the paper. Width of figure should be 84 mm (one column). Contrast of photos or graphs should be at least 600 dpi. Contrast of line drawings should be at least 1,200 dpi. The Powerpoint file (ppt, pptx) is also acceptable.”

Unfortunately, without sufficient knowledge of computer graphics, it is not easy to understand the submission requirement above. Therefore, it is necessary to develop an understanding of image resolution, image format (bitmap and vector images), and the corresponding file specifications.

Resolution is often mentioned to describe the quality of images containing graphs or CT/MRI scans, and video files. The higher the resolution, the clearer and closer to reality the image is, while the opposite is true for low resolutions. The most representative unit used to describe a resolution is “dpi” (dots per inch): this literally translates to the number of dots required to constitute 1 inch. The greater the number of dots, the higher the resolution. The KJA submission requirements recommend 600 dpi for images, and 1,200 dpi 4) for graphs. In other words, resolutions in which 600 or 1,200 dots constitute one inch are required for submission.

There are requirements for the horizontal length of an image in addition to the resolution requirements. While there are no requirements for the vertical length of an image, it must not exceed the vertical length of a page. The width of a column on one side of a printed page is 84 mm, or 3.3 inches (84/25.4 mm ≒ 3.3 inches). Therefore, a graph must have a resolution in which 1,200 dots constitute 1 inch, and have a width of 3.3 inches.

Bitmap and Vector

Methods of image construction are important. Bitmap images can be considered as images drawn on section paper. Enlarging the image will enlarge the picture along with the grid, resulting in a lower resolution; in other words, aliasing occurs. On the other hand, reducing the size of the image will reduce the size of the picture, while increasing the resolution. In other words, resolution and the size of an image are inversely proportionate to one another in bitmap images, and it is a drawback of bitmap images that resolution must be considered when adjusting the size of an image. To enlarge an image while maintaining the same resolution, the size and resolution of the image must be determined before saving the image. An image that has already been created cannot avoid changes to its resolution according to changes in size. Enlarging an image while maintaining the same resolution will increase the number of horizontal and vertical dots, ultimately increasing the number of pixels 5) of the image, and the file size. In other words, the file size of a bitmap image is affected by the size and resolution of the image (file extensions include JPG [JPEG] 6) , PNG 7) , GIF 8) , and TIF [TIFF] 9) . To avoid this complexity, the width of an image can be set to 4 inches and its resolution to 900 dpi to satisfy the submission requirements of most journals [ 12 ].

Vector images overcome the shortcomings of bitmap images. Vector images are created based on mathematical operations of line segments and areas between different points, and are not affected by aliasing or pixelation. Furthermore, they result in a smaller file size that is not affected by the size of the image. They are commonly used for drawings and illustrations (file extensions include EPS 10) , CGM 11) , and SVG 12) ).

Finally, the PDF 13) is a file format developed by Adobe Systems (Adobe Systems, CA, USA) for electronic documents, and can contain general documents, text, drawings, images, and fonts. They can also contain bitmap and vector images. While vector images are used by researchers when working in Powerpoint, they are saved as 960 × 720 dots when saved in TIFF format in Powerpoint. This results in a resolution that is inappropriate for printing on a paper medium. To save high-resolution bitmap images, the image must be saved as a PDF file instead of a TIFF, and the saved PDF file must be imported into an imaging processing program such as Photoshop™(Adobe Systems, CA, USA) to be saved in TIFF format [ 12 ].

1) Instructions to authors in KJA; section 5-(9) Table; https://ekja.org/index.php?body=instruction

2) Instructions to Authors in KJA; section 6-1)-(10) Figures and illustrations in Manuscript preparation; https://ekja.org/index.php?body=instruction

3) Instructions to Authors in KJA; section 6-1)-(10) Figures and illustrations in Manuscript preparation; https://ekja.org/index.php?body=instruction

4) Resolution; in KJA, it is represented by “contrast.”

5) Pixel is a minimum unit of an image and contains information of a dot and color. It is derived by multiplying the number of vertical and horizontal dots regardless of image size. For example, Full High Definition (FHD) monitor has 1920 × 1080 dots ≒ 2.07 million pixel.

6) Joint Photographic Experts Group.

7) Portable Network Graphics.

8) Graphics Interchange Format

9) Tagged Image File Format; TIFF

10) Encapsulated PostScript.

11) Computer Graphics Metafile.

12) Scalable Vector Graphics.

13) Portable Document Format.

Advantages and Disadvantages of Graphical Representation of Data

The graphical view is vastly used in every type of data or report. It makes data easier to understand and also has a lot more advantages like this. But it also has some disadvantages so for that reason, we are giving here some advantages and disadvantages of graphical representation of data.

Everyone should know the advantages and disadvantages of the graphical representation of data because some people are not aware of the disadvantages of the graphical representation of data. This article will clear the concept of those people.

Advantages of Graphical Representation of Data

Graphical representation of reports enjoys various advantages which are as follows:

1. Acceptability : Such a report is acceptable to busy persons because it easily highlights the theme of the report. This helps to avoid waste of time.

2. Comparative Analysis : Information can be compared in terms of graphical representation. Such comparative analysis helps for quick understanding and attention.

3. Less cost : Information if descriptive involves huge time to present properly. It involves more money to print the information but the graphical presentation can be made in a short but catchy view to make the report understandable. It obviously involves less cost.

4. Decision Making : Business executives can view the graphs at a glance and can make a decision very quickly which is hardly possible through descriptive reports.

5. Logical Ideas : If tables, designs, and graphs are used to represent information then a logical sequence is created to clear the idea of the audience.

6. Helpful for less literate Audience : Less literate or illiterate people can understand graphical representation easily because it does not involve going through line-by-line and descriptive reports.

7. Less Effort and Time : To present any table, design, image, or graph require less effort and time. Furthermore, such a presentation makes a quick understanding of the information.

8. Less Error and Mistakes : Qualitative or informative or descriptive reports involve errors or mistakes. As graphical representations are exhibited through numerical figures, tables, or graphs, it usually involves fewer errors and mistakes.

9. A complete Idea : Such representation creates a clear and complete idea in the mind of the audience. Reading a hundred pages may not give any scope to make a decision. But an instant view or looking at a glance obviously makes an impression in the mind of the audience regarding the topic or subject.

10. Use in the Notice Board : Such representation can be hung on the notice board to quickly raise the attention of employees in any organization.

Disadvantages of Graphical Representation of Data

The graphical representation of reports is not free from limitations. The following are the problems with a graphical representation of data or reports:

1. Costly : Graphical representation of reports is costly because it involves images, colors, and paints. A combination of material with human efforts makes the graphical presentation expensive.

2. More time : Normal report involves less time to represent but graphical representation involves more time as it requires graphs and figures which are dependent on more time.

3. Errors and Mistakes : Since graphical representations are complex, there is- each and every chance of errors and mistakes. This causes problems for a better understanding of general people.

4. Lack of Secrecy : Graphical representation makes the full presentation of information that may hamper the objective to keep something secret.

5. Problems to select a suitable method : Information can be presented through various graphical methods and ways. Which should be the suitable method is very hard to select.

6. The problem of Understanding : All may not be able to get the meaning of graphical representation because it involves various technical matters which are complex to general people.

Last, of all, it can be said that graphical representation does not provide proper information to general people.

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6 thoughts on “Advantages and Disadvantages of Graphical Representation of Data”

the answers are very good in maybe answering a question on the advantages and disadvantage of using graphical representation of reporting a research findings, as compared to using simple reporting numbers

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2.E: Graphical Representations of Data (Exercises)

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2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs

Student grades on a chemistry exam were: 77, 78, 76, 81, 86, 51, 79, 82, 84, 99

• Construct a stem-and-leaf plot of the data.
• Are there any potential outliers? If so, which scores are they? Why do you consider them outliers?

The table below contains the 2010 obesity rates in U.S. states and Washington, DC.

• Use a random number generator to randomly pick eight states. Construct a bar graph of the obesity rates of those eight states.
• Construct a bar graph for all the states beginning with the letter "A."
• Construct a bar graph for all the states beginning with the letter "M."
• Number the entries in the table 1–51 (Includes Washington, DC; Numbered vertically)
• Arrow over to PRB
• Press 5:randInt(
• Enter 51,1,8)

Eight numbers are generated (use the right arrow key to scroll through the numbers). The numbers correspond to the numbered states (for this example: {47 21 9 23 51 13 25 4}. If any numbers are repeated, generate a different number by using 5:randInt(51,1)). Here, the states (and Washington DC) are {Arkansas, Washington DC, Idaho, Maryland, Michigan, Mississippi, Virginia, Wyoming}.

Corresponding percents are {30.1, 22.2, 26.5, 27.1, 30.9, 34.0, 26.0, 25.1}.

Figure \(\PageIndex{1}\): (a)

Figure \(\PageIndex{1}\): (b)

Figure \(\PageIndex{1}\): (c)

For each of the following data sets, create a stem plot and identify any outliers.

Exercise 2.2.7

The miles per gallon rating for 30 cars are shown below (lowest to highest).

19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43

The height in feet of 25 trees is shown below (lowest to highest).

25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

The data are the prices of different laptops at an electronics store. Round each value to the nearest ten.

249, 249, 260, 265, 265, 280, 299, 299, 309, 319, 325, 326, 350, 350, 350, 365, 369, 389, 409, 459, 489, 559, 569, 570, 610

The data are daily high temperatures in a town for one month.

61, 61, 62, 64, 66, 67, 67, 67, 68, 69, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 95

For the next three exercises, use the data to construct a line graph.

Exercise 2.2.8

In a survey, 40 people were asked how many times they visited a store before making a major purchase. The results are shown in the Table below.

Exercise 2.2.9

In a survey, several people were asked how many years it has been since they purchased a mattress. The results are shown in Table .

Exercise 2.2.10

Several children were asked how many TV shows they watch each day. The results of the survey are shown in the Table below.

Exercise 2.2.11

The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. Table shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students.

Using the data from Mrs. Ramirez’s math class supplied in the table above, construct a bar graph showing the percentages.

Exercise 2.2.12

David County has six high schools. Each school sent students to participate in a county-wide science competition. Table shows the percentage breakdown of competitors from each school, and the percentage of the entire student population of the county that goes to each school. Construct a bar graph that shows the population percentage of competitors from each school.

Use the data from the David County science competition supplied in Exercise . Construct a bar graph that shows the county-wide population percentage of students at each school.

2.3: Histograms, Frequency, Polygons, and Time Series Graphs

Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:

• Find the relative frequencies for each survey. Write them in the charts.
• Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.
• In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
• Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
• Make new histograms for Publisher A and Publisher B. This time, make bar widths of two.
• Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer.

Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all onboard transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Following is a summary of the bills for each group.

• Fill in the relative frequency for each group.
• Construct a histogram for the singles group. Scale the x -axis by $50 widths. Use relative frequency on the y -axis.
• Construct a histogram for the couples group. Scale the x -axis by $50 widths. Use relative frequency on the y -axis.
• List two similarities between the graphs.
• List two differences between the graphs.
• Overall, are the graphs more similar or different?
• Construct a new graph for the couples by hand. Since each couple is paying for two individuals, instead of scaling the x -axis by $50, scale it by $100. Use relative frequency on the y -axis.
• How did scaling the couples graph differently change the way you compared it to the singles graph?
• Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple? Explain why in one or two complete sentences.
• See the tables above

• Both graphs have a single peak.
• Both graphs use class intervals with width equal to $50.
• The couples graph has a class interval with no values.
• It takes almost twice as many class intervals to display the data for couples.
• Answers may vary. Possible answers include: The graphs are more similar than different because the overall patterns for the graphs are the same.
• Check student's solution.
• Both graphs display 6 class intervals.
• Both graphs show the same general pattern.
• Answers may vary. Possible answers include: Although the width of the class intervals for couples is double that of the class intervals for singles, the graphs are more similar than they are different.
• Answers may vary. Possible answers include: You are able to compare the graphs interval by interval. It is easier to compare the overall patterns with the new scale on the Couples graph. Because a couple represents two individuals, the new scale leads to a more accurate comparison.
• Answers may vary. Possible answers include: Based on the histograms, it seems that spending does not vary much from singles to individuals who are part of a couple. The overall patterns are the same. The range of spending for couples is approximately double the range for individuals.

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.

• Construct a histogram of the data.
• Complete the columns of the chart.

Use the following information to answer the next two exercises: Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.

The percentage of people who own at most three t-shirts costing more than $19 each is approximately:

• Cannot be determined

If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:

• simple random
• convenience

Following are the 2010 obesity rates by U.S. states and Washington, DC.

Construct a bar graph of obesity rates of your state and the four states closest to your state. Hint: Label the \(x\)-axis with the states.

Answers will vary.

Exercise 2.3.6

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table.

Exercise 2.3.7

What does the frequency column in the Table above sum to? Why?

Exercise 2.3.8

What does the relative frequency column in in the Table above  sum to? Why?

Exercise 2.3.9

What is the difference between relative frequency and frequency for each data value in in the Table above ?

The relative frequency shows the proportion of data points that have each value. The frequency tells the number of data points that have each value.

Exercise 2.3.10

What is the difference between cumulative relative frequency and relative frequency for each data value?

Exercise 2.3.11

To construct the histogram for the data in in the Table above , determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram. Label the horizontal and vertical axes with words. Include numerical scaling.

Answers will vary. One possible histogram is shown:

Exercise 2.3.12

Construct a frequency polygon for the following:

Exercise 2.3.13

Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger.

Find the midpoint for each class. These will be graphed on the x -axis. The frequency values will be graphed on the y -axis values.

Exercise 2.3.14

Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men?

Exercise 2.3.15

Construct a times series graph for (a) the number of male births, (b) the number of female births, and (c) the total number of births.

Exercise 2.3.16

The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to 1973.

• Construct a double time series graph using a common x -axis for both sets of data.
• Which variable increased the fastest? Explain.
• Did Detroit’s increase in police officers have an impact on the murder rate? Explain.

2.4: Measures of the Location of the Data

The median age for U.S. blacks currently is 30.9 years; for U.S. whites it is 42.3 years.

• Based upon this information, give two reasons why the black median age could be lower than the white median age.
• Does the lower median age for blacks necessarily mean that blacks die younger than whites? Why or why not?
• How might it be possible for blacks and whites to die at approximately the same age, but for the median age for whites to be higher?

Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?" The results are in the Table below. Also, include left endpoint, but not the right endpoint.

• What percentage of the survey answered "not sure"?
• What percentage think that middle-class is from $25,000 to $50,000?
• Should all bars have the same width, based on the data? Why or why not?
• How should the <20,000 and the 100,000+ intervals be handled? Why?
• Find the 40 th and 80 th percentiles
• Construct a bar graph of the data
• \(1 - (0.02 + 0.09 + 0.19 + 0.26 + 0.18 + 0.17 + 0.02 + 0.01) = 0.06\)
• \(0.19 + 0.26 + 0.18 = 0.63\)
• Check student’s solution.

80 th percentile will fall between 50,000 and 75,000

Given the following box plot:

• which quarter has the smallest spread of data? What is that spread?
• which quarter has the largest spread of data? What is that spread?
• find the interquartile range ( IQR ).
• are there more data in the interval 5–10 or in the interval 10–13? How do you know this?
• 10–12
• 12–13
• need more information

The following box plot shows the U.S. population for 1990, the latest available year.

• Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know?
• 12.6% are age 65 and over. Approximately what percentage of the population are working age adults (above age 17 to age 65)?
• more children; the left whisker shows that 25% of the population are children 17 and younger. The right whisker shows that 25% of the population are adults 50 and older, so adults 65 and over represent less than 25%.

2.5: Box Plots

In a survey of 20-year-olds in China, Germany, and the United States, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.

• In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected.
• Have more Americans or more Germans surveyed been to over eight foreign countries?
• Compare the three box plots. What do they imply about the foreign travel of 20-year-old residents of the three countries when compared to each other?

Given the following box plot, answer the questions.

• Think of an example (in words) where the data might fit into the above box plot. In 2–5 sentences, write down the example.
• What does it mean to have the first and second quartiles so close together, while the second to third quartiles are far apart?
• Answers will vary. Possible answer: State University conducted a survey to see how involved its students are in community service. The box plot shows the number of community service hours logged by participants over the past year.
• Because the first and second quartiles are close, the data in this quarter is very similar. There is not much variation in the values. The data in the third quarter is much more variable, or spread out. This is clear because the second quartile is so far away from the third quartile.

Given the following box plots, answer the questions.

• Data 1 has more data values above two than Data 2 has above two.
• The data sets cannot have the same mode.
• For Data 1 , there are more data values below four than there are above four.
• For which group, Data 1 or Data 2, is the value of “7” more likely to be an outlier? Explain why in complete sentences.

A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.

• In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.
• Which group is most likely to have an outlier? Explain how you determined that.
• Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?
• Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?
• Look at the BMW 5 series. Which quarter has the largest spread of data? What is the spread?
• Look at the BMW 5 series. Estimate the interquartile range (IQR).
• Look at the BMW 5 series. Are there more data in the interval 31 to 38 or in the interval 45 to 55? How do you know this?
• 31–35
• 38–41
• 41–64
• Each box plot is spread out more in the greater values. Each plot is skewed to the right, so the ages of the top 50% of buyers are more variable than the ages of the lower 50%.
• The BMW 3 series is most likely to have an outlier. It has the longest whisker.
• Comparing the median ages, younger people tend to buy the BMW 3 series, while older people tend to buy the BMW 7 series. However, this is not a rule, because there is so much variability in each data set.
• The second quarter has the smallest spread. There seems to be only a three-year difference between the first quartile and the median.
• The third quarter has the largest spread. There seems to be approximately a 14-year difference between the median and the third quartile.
• IQR ~ 17 years
• There is not enough information to tell. Each interval lies within a quarter, so we cannot tell exactly where the data in that quarter is concentrated.
• The interval from 31 to 35 years has the fewest data values. Twenty-five percent of the values fall in the interval 38 to 41, and 25% fall between 41 and 64. Since 25% of values fall between 31 and 38, we know that fewer than 25% fall between 31 and 35.

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

Construct a box plot of the data.

2.6: Measures of the Center of the Data

The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the following table.

• What is the best estimate of the average obesity percentage for these countries?
• The United States has an average obesity rate of 33.9%. Is this rate above average or below?
• How does the United States compare to other countries?

The table below gives the percent of children under five considered to be underweight. What is the best estimate for the mean percentage of underweight children?

The mean percentage, \(\bar{x} = \frac{1328.65}{50} = 26.75\)

2.7: Skewness and the Mean, Median, and Mode

The median age of the U.S. population in 1980 was 30.0 years. In 1991, the median age was 33.1 years.

• What does it mean for the median age to rise?
• Give two reasons why the median age could rise.
• For the median age to rise, is the actual number of children less in 1991 than it was in 1980? Why or why not?

2.8: Measures of the Spread of the Data

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.

• \(\mu = 1000\) FTES
• median = 1,014 FTES
• \(\sigma = 474\) FTES
• first quartile = 528.5 FTES
• third quartile = 1,447.5 FTES
• \(n = 29\) years

A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer.

The median value is the middle value in the ordered list of data values. The median value of a set of 11 will be the 6th number in order. Six years will have totals at or below the median.

75% of all years have an FTES:

• at or below: _____
• at or above: _____

The population standard deviation = _____

What percent of the FTES were from 528.5 to 1447.5? How do you know?

What is the IQR ? What does the IQR represent?

How many standard deviations away from the mean is the median?

Additional Information: The population FTES for 2005–2006 through 2010–2011 was given in an updated report. The data are reported here.

Calculate the mean, median, standard deviation, the first quartile, the third quartile and the IQR . Round to one decimal place.

• mean = 1,809.3
• median = 1,812.5
• standard deviation = 151.2
• first quartile = 1,690
• third quartile = 1,935

Construct a box plot for the FTES for 2005–2006 through 2010–2011 and a box plot for the FTES for 1976–1977 through 2004–2005.

Compare the IQR for the FTES for 1976–77 through 2004–2005 with the IQR for the FTES for 2005-2006 through 2010–2011. Why do you suppose the IQR s are so different?

Hint: Think about the number of years covered by each time period and what happened to higher education during those periods.

Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best GPA when compared to other students at his school? Explain how you determined your answer.

A music school has budgeted to purchase three musical instruments. They plan to purchase a piano costing $3,000, a guitar costing $550, and a drum set costing $600. The mean cost for a piano is $4,000 with a standard deviation of $2,500. The mean cost for a guitar is $500 with a standard deviation of $200. The mean cost for drums is $700 with a standard deviation of $100. Which cost is the lowest, when compared to other instruments of the same type? Which cost is the highest when compared to other instruments of the same type. Justify your answer.

For pianos, the cost of the piano is 0.4 standard deviations BELOW the mean. For guitars, the cost of the guitar is 0.25 standard deviations ABOVE the mean. For drums, the cost of the drum set is 1.0 standard deviations BELOW the mean. Of the three, the drums cost the lowest in comparison to the cost of other instruments of the same type. The guitar costs the most in comparison to the cost of other instruments of the same type.

An elementary school class ran one mile with a mean of 11 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in eight minutes. A junior high school class ran one mile with a mean of nine minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran one mile with a mean of seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.

• Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
• Who is the fastest runner with respect to his or her class? Explain why.

The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the table belo2

What is the best estimate of the average obesity percentage for these countries? What is the standard deviation for the listed obesity rates? The United States has an average obesity rate of 33.9%. Is this rate above average or below? How “unusual” is the United States’ obesity rate compared to the average rate? Explain.

• \(\bar{x} = 23.32\)
• Using the TI 83/84, we obtain a standard deviation of: \(s_{x} = 12.95\).
• The obesity rate of the United States is 10.58% higher than the average obesity rate.
• Since the standard deviation is 12.95, we see that \(23.32 + 12.95 = 36.27\) is the obesity percentage that is one standard deviation from the mean. The United States obesity rate is slightly less than one standard deviation from the mean. Therefore, we can assume that the United States, while 34% obese, does not have an unusually high percentage of obese people.

The Table below gives the percent of children under five considered to be underweight.

What is the best estimate for the mean percentage of underweight children? What is the standard deviation? Which interval(s) could be considered unusual? Explain.

• Accountancy
• Business Studies
• Commercial Law
• Organisational Behaviour
• Human Resource Management
• Entrepreneurship
• CBSE Class 11 Statistics for Economics Notes

Chapter 1: Concept of Economics and Significance of Statistics in Economics

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Data Collection & Its Methods
• Sources of Data Collection | Primary and Secondary Sources
• Direct Personal Investigation: Meaning, Suitability, Merits, Demerits and Precautions
• Indirect Oral Investigation : Suitability, Merits, Demerits and Precautions
• Difference between Direct Personal Investigation and Indirect Oral Investigation
• Information from Local Source or Correspondents: Meaning, Suitability, Merits, and Demerits
• Questionnaires and Schedules Method of Data Collection
• Difference between Questionnaire and Schedule
• Qualities of a Good Questionnaire and types of Questions
• What are the Published Sources of Collecting Secondary Data?
• What Precautions should be taken before using Secondary Data?
• Two Important Sources of Secondary Data: Census of India and Reports & Publications of NSSO
• What is National Sample Survey Organisation (NSSO)?
• What is Census Method of Collecting Data?
• Sample Method of Collection of Data
• Methods of Sampling
• Father of Indian Census
• What makes a Sampling Data Reliable?
• Difference between Census Method and Sampling Method of Collecting Data
• What are Statistical Errors?

Chapter 3: Organisation of Data

• Organization of Data
• Objectives and Characteristics of Classification of Data
• Classification of Data in Statistics | Meaning and Basis of Classification of Data
• Concept of Variable and Raw Data
• Types of Statistical Series
• Difference between Frequency Array and Frequency Distribution
• Types of Frequency Distribution

Chapter 4: Presentation of Data: Textual and Tabular

Textual presentation of data: meaning, suitability, and drawbacks.

• Tabular Presentation of Data: Meaning, Objectives, Features and Merits
• Different Types of Tables
• Classification and Tabulation of Data

Chapter 5: Diagrammatic Presentation of Data

• Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages
• Types of Diagrams
• Bar Graph | Meaning, Types, and Examples
• Pie Diagrams | Meaning, Example and Steps to Construct
• Histogram | Meaning, Example, Types and Steps to Draw
• Frequency Polygon | Meaning, Steps to Draw and Examples
• Ogive (Cumulative Frequency Curve) and its Types
• What is Arithmetic Line-Graph or Time-Series Graph?
• Diagrammatic and Graphic Presentation of Data

Chapter 6: Measures of Central Tendency: Arithmetic Mean

• Measures of Central Tendency in Statistics
• Arithmetic Mean: Meaning, Example, Types, Merits, and Demerits
• What is Simple Arithmetic Mean?
• Calculation of Mean in Individual Series | Formula of Mean
• Calculation of Mean in Discrete Series | Formula of Mean
• Calculation of Mean in Continuous Series | Formula of Mean
• Calculation of Arithmetic Mean in Special Cases
• Weighted Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

• Median(Measures of Central Tendency): Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Median for Different Types of Statistical Series
• Calculation of Median in Individual Series | Formula of Median
• Calculation of Median in Discrete Series | Formula of Median
• Calculation of Median in Continuous Series | Formula of Median
• Graphical determination of Median
• Mode: Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Mode in Individual Series | Formula of Mode
• Calculation of Mode in Discrete Series | Formula of Mode
• Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
• Calculation of Mode in Continuous Series | Formula of Mode
• Calculation of Mode in Special Cases
• Calculation of Mode by Graphical Method
• Mean, Median and Mode| Comparison, Relationship and Calculation

Chapter 8: Measures of Dispersion

• Measures of Dispersion | Meaning, Absolute and Relative Measures of Dispersion
• Range | Meaning, Coefficient of Range, Merits and Demerits, Calculation of Range
• Calculation of Range and Coefficient of Range
• Interquartile Range and Quartile Deviation
• Partition Value | Quartiles, Deciles and Percentiles
• Quartile Deviation and Coefficient of Quartile Deviation: Meaning, Formula, Calculation, and Examples
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Standard Deviation: Meaning, Coefficient of Standard Deviation, Merits, and Demerits
• Standard Deviation in Individual Series
• Methods of Calculating Standard Deviation in Discrete Series
• Methods of calculation of Standard Deviation in frequency distribution series
• Combined Standard Deviation: Meaning, Formula, and Example
• How to calculate Variance?
• Coefficient of Variation: Meaning, Formula and Examples
• Lorenz Curveb : Meaning, Construction, and Application

Chapter 9: Correlation

• Correlation: Meaning, Significance, Types and Degree of Correlation
• Methods of measurements of Correlation
• Calculation of Correlation with Scattered Diagram
• Spearman's Rank Correlation Coefficient
• Karl Pearson's Coefficient of Correlation
• Karl Pearson's Coefficient of Correlation | Methods and Examples

Chapter 10: Index Number

• Index Number | Meaning, Characteristics, Uses and Limitations
• Methods of Construction of Index Number
• Unweighted or Simple Index Numbers: Meaning and Methods
• Methods of calculating Weighted Index Numbers
• Fisher's Index Number as an Ideal Method
• Fisher's Method of calculating Weighted Index Number
• Paasche's Method of calculating Weighted Index Number
• Laspeyre's Method of calculating Weighted Index Number
• Laspeyre's, Paasche's, and Fisher's Methods of Calculating Index Number
• Consumer Price Index (CPI) or Cost of Living Index Number: Construction of Consumer Price Index|Difficulties and Uses of Consumer Price Index
• Methods of Constructing Consumer Price Index (CPI)
• Wholesale Price Index (WPI) | Meaning, Uses, Merits, and Demerits
• Index Number of Industrial Production : Characteristics, Construction & Example
• Inflation and Index Number

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

Presentation of Data refers to the exhibition of data in such a clear and attractive way that it is easily understood and analysed. Data can be presented in different forms, including Textual or Descriptive Presentation, Tabular Presentation, and Diagrammatic Presentation.

Textual Presentation

Textual or Descriptive Presentation of Data is one of the most common forms of data presentation. In this, data is a part of the text of the study or a part of the description of the subject matter of the study. It is usually preferred when the quantity of data is not very large. For example, there are 50 students in a class, among them 30 are boys and 20 are girls. This is the data that can be understood with the help of a simple text and no table or pie diagram is required for the same. 

Suitability

Textual Presentation of Data is suitable when the quantity of data is not large. It means that a small portion of data that is presented as a part of the subject matter of study can become useful supportive evidence to the given text. Therefore, instead of saying that the price of petrol is skyrocketing, it can be said that the price of petrol has increased by 20% in the last 2 years, and this statement will be more meaningful and precise. Under textual presentation of data, an individual does not have to support the text with the help of a diagram or table as the text in itself is very small and has few observations. 

Advantages of Textual Presentation of Data

Textual Presentation of Data has the following benefits:

1. It allows the researcher to make an elaborate interpretation of data during the presentation. 

2. A researcher can easily present qualitative data that cannot be presented in tabular or graphical form using the textual presentation of data. 

3. If the data is present in small sets, a textual presentation can be easily used. For example, there are 50 students in a class, among them, 30 are boys and 20 are girls. This is the data that can be understood with the help of a simple text and no table or pie diagram is required for the same. 

Disadvantages of Textual Presentation of Data

Textual Presentation of Data has the following drawbacks:

1. One of the major drawbacks of the textual presentation of data is that it provides extensive data in the form of text and paragraphs which makes it difficult for the user of data to draw a proper conclusion at a glance. This facility is provided in tabular or diagrammatic presentation of data.

2. This method of presenting data is not suitable for large sets of data as these sets contain too many details. 

3. Besides, one has to read through the whole text in order to understand and comprehend the main point of the data.

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U.S. Job Growth Much Stronger Than Expected

Employers added 303,000 jobs in March, the 39th straight month of growth. The unemployment rate fell to 3.8 percent.

• Share full article

Monthly change in jobs

+303,000 jobs

+300,000 jobs

March ’23

March ’24

Talmon Joseph Smith

Here’s what to know about the jobs report.

Another month, another burst of strong job gains. Employers added 303,000 jobs in March on a seasonally adjusted basis, the Labor Department reported on Friday.

It was the 39th straight month of job growth and a much larger gain than forecast. The unemployment rate fell to 3.8 percent, from 3.9 percent in February.

The continuing strength, labor market analysts say, may increase confidence among investors and the Federal Reserve that the U.S. economy has reached a healthy equilibrium in which a steady roll of commercial activity, growing employment and rising wages coexist.

It’s a remarkable change from a year ago, when top financial analysts were largely convinced that a recession was only months away.

From late 2021 to early 2023, inflation was outstripping wage gains, but that also now appears to have firmly shifted, even as wage increases cool from their peak rates of growth in 2022. Average hourly earnings for workers rose 0.3 percent in March from the previous month and were up 4.1 percent from March 2023.

Revisions to employment data in recent months showed a total uptick of 22,000 jobs.

Some analysts were worried about a trend in one of the two surveys that the government uses to track the labor market: out of step with most other data on job growth and layoffs, it showed weak hiring rates that, if correct, would have probably indicated an economy “already in recession,” according to the economic research team at Bank of America.

But even that worrying bit of outlier data improved in the latest report.

“The vanishingly few areas to criticize this labor market are melting away,” said Andrew Flowers, a labor economist at Appcast, a recruitment advertising firm.

Some have worried that as the booming labor market recovery transitioned into a slower expansion, job growth would mostly narrow to less cyclical sectors like government hiring and health care. Gains in health care — including hospitals, nursing and residential care facilities and outpatient services — led the way in this report, but job growth, for now, remains broad-based.

The private sector added 232,000 jobs overall. Construction added 39,000 jobs in March, about twice its average monthly gain in the past year. Employment in hospitality and leisure, which plunged during the pandemic, continues to bounce back and is now above its February 2020 levels.

The “continued vigor,” said Joe Davis, the global chief economist at Vanguard, has come from “household balance sheets bolstered by pandemic-related fiscal policy and a virtuous cycle where job growth, wages and consumption fuel one another.”

Data analysts note that better-than-expected gains in business productivity and work force participation have added fuel, too. Businesses large and small have had to navigate an obstacle course this decade: a pandemic, inflationary pressures and a steep rise in the cost of credit. But recently released data from the Bureau of Economic Analysis shows corporate profits have reached a record high.

Officials at the Fed, which rapidly raised interest rates in 2022 and early 2023 to combat inflation, have expressed cautious optimism that they are approaching their goals of low unemployment and more stable prices.

Inflation has fallen drastically from its peak of 7.1 percent, according to the Fed’s preferred measure . But it ticked up in February to 2.5 percent, still a half-percentage point away from the Fed’s target. And some worry that rising oil prices or geopolitical chaos could upend the delicate state of affairs.

Sal Gilbertie, the chief executive at Teucrium Trading, which covers commodities markets, said he thinks that energy prices could do a “touch higher on oil if Ukraine keeps the pressure on Russia and economic numbers remain healthy.”

Joe Rennison

U.S. government bond yields, which underpin interest rates throughout the economy, are higher, with the 10-year Treasury yield up 0.07 percentage points, to 4.37 percent.

Expectations for rate cuts have also come under pressure, with investors dialing down the prospect of a rate cut in June.

The S&P 500 rose 0.5 percent in early trading. It seems investors are continuing to focus on the signs of a robust economy that could support corporate profits, rather than on stubborn inflation keeping interest rates elevated for longer.

S&P 500

And while the stock index is still on course for its worst weekly performance since October, after a drop on Thursday, it remains close to its record high.

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Jeanna Smialek

“While I don’t see the economy overheating, the Fed knows how to respond if it does,” Thomas Barkin, president of the Richmond Fed, said during a speech following the jobs report. He noted that the fresh data reaffirmed that the job market is strong.

Lydia DePillis

As Jeanna noted earlier, immigration has been a strong undercurrent in the labor market over the past year. For a few months, it was starting to look as though unemployment was rising among immigrants — potentially a sign that new arrivals were having a hard time finding jobs — but it sank back down in March and now sits below the unemployment rate for native-born workers.

President Biden declared the report a “milestone,” noting that the economy has created 15 million jobs since he took office. He also noted the length of time unemployment has been below 4 percent, which is generally seen as a threshold of full employment. “We’ve come a long way, but I won’t stop fighting for hardworking families,” he said in a statement, ticking down a list of his administration’s actions to lower costs for consumers.

Economists think that the job market can sustainably add more jobs these days because immigration has been really strong, adding to the supply of available workers. But 303,000 is still quicker than most of those estimates: Brookings has suggested the sustainable level is in the ballpark of 160,000 to 200,000, and even optimistic calls like Morgan Stanley’s 265,000 are lower than the March hiring increase.

J. Edward Moreno

Despite the strong jobs data, some companies that reported earnings in recent weeks have said they are pulling back on hiring because of the high cost of labor. Paychex, a payroll software company, said its clients were struggling to find the right talent.

“Our clients tell us they still can’t find qualified employees and are not willing to hire just anyone at higher wage rates, especially in areas with recent minimum wage increases and aggressive legislative changes,” said John Bradley Gibson, chief executive of Paychex.

Indeed, as Edward mentioned, companies have been talking up their “rightsizing” measures. According to S&P Global Market Intelligence this week, “Profitability mentions may be related to cost cutting measures, as talk of layoffs (and related terms) increased by 24 percent.”

Ben Casselman

One concern about the job market lately is that hiring has been concentrated in a few sectors: leisure and hospitality, health care and social assistance, and government. Those accounted for two-thirds of the gains in March, but construction and retail also added a substantial number of jobs.

Hiring jumped across industries

Change in jobs in March 2024, by sector

+88,000 jobs

Education and health

Leisure and

hospitality

Construction

Manufacturing

Leisure and hospitality

Business services

Thomas Simons, a U.S. economist at Jefferies who has been expecting further deceleration in the labor market, was frank in a note to clients. “The data leaves us borderline speechless,” he wrote. “We don’t want to overreact to one single data release, especially one that has the reliability issues and revision risk that this one does, but this calls our bear case for the economy into question.”

The Labor Department’s broader measure of unemployment, which includes people who are working part-time for economic reasons and want a job but aren’t actively looking, remained stable at 7.3 percent. But in one of the more concrete signs that the labor market isn’t as tight as it was a year ago, that’s substantially above where it was last March, at 6.7 percent.

The Fed has recently welcomed strong jobs gains as labor supply picks up.

Year-over-year percentage change in earnings vs. inflation

+4.1% in March

+3.2% in Feb.

Consumer Price Index

Avg. hourly earnings

Federal Reserve officials spent much of 2022 and 2023 worried that the job market was too strong to be sustainable. Employers were racing to snap up a limited supply of workers, the logic went, leading to rapid wage gains that would eventually prod those companies to raise prices to cover their labor costs.

But instead of viewing rapid job gains as a potentially inflationary problem, the Fed has recently embraced them.

That is because strong hiring has come alongside a marked pickup in labor supply. Immigration has been much stronger than expected, and millennial men and women in particular are trickling into the labor force, enabling companies to hire without having to compete too fiercely for employees. Wage growth has been strong but not gangbusters, and inflation has cooled across a range of purchases, including those in service categories that are typically sensitive to labor costs.

Data released Friday showed that a lot of those trends persist. Hiring was very strong in March, and that wages climbed at a solid clip but continued to moderate somewhat on an annual basis. Average hourly earnings climbed by 4.1 percent last month compared to a year earlier, a tick down from 4.3 percent in February.

Overall labor force participation picked up slightly, meaning that a greater share of adults were working or looking for jobs, and employment among foreign-born workers continued to climb — a hint that immigrants may have accounted for some of the solid job increase.

The question now is how long policymakers will remain willing to tolerate such strong hiring without worrying that it will cause consumer demand, economic growth and inflation to pick back up. Job gains at the pace seen in March is faster than what most economists think is sustainable, even accounting for increasing labor supply.

But in recent speeches, central bankers have mostly signaled comfort with the vigorous labor market.

The job market is “strong but rebalancing,” Jerome H. Powell, the Fed chair, said in a speech this week . He noted that job openings had come down and that employers were reporting in surveys more ease in hiring.

A balanced but robust job market is good news for the Fed. If businesses are managing to find workers to hire, it means the economy can grow at a solid pace without overheating and generating a lot of inflation. And that means that the Fed can squeeze the economy a little bit with higher interest rates — something it is doing to wrestle inflation under control — without slamming on the brakes.

In fact, the recent surprising jump in worker supply is a big reason that the central bank might pull off a “soft landing,” in which it sets the labor market down gently and without causing a painful recession. Mr. Powell noted this week that immigration was a big reason that the economy blew through forecasters’ expectations for growth last year without generating inflation.

In fact, price increases cooled from 6.4 percent headed into the year to 3.3 percent at its conclusion, even as consumer spending consistently beat predictions.

“Our economy has been short labor, and probably still is,” Mr. Powell said, but immigration “explains what we’ve been asking ourselves, which is, ‘How can the economy have grown over 3 percent in a year where almost every outside economist was forecasting a recession?’”

Still, the current pace of jobs growth is strong even once rapid immigration is accounted for, which could keep Fed officials wary that the economy is still at risk of overheating if hiring continues at this pace.

Economists think that as immigration adds to the labor supply, job growth can remain strong without overheating the economy. A Brookings Institution analysis recently estimated that employers could add 160,000 to 200,000 jobs per month this year without a big risk of wages spiking and inflation rising. Without all of the immigration, that would have been more like 60,000 to 100,000.

And some Fed officials have already been questioning whether the central bank should cut rates at a time when inflation is proving stubborn and the economy looks like it might be heating back up.

Fed policymakers have been suggesting for months that they could soon cut borrowing costs, which are now set to about 5.3 percent. But as inflation has hit a sticking point after months of deceleration, investors have been steadily pushing back their expectation for when that might happen, and now expect the first move in only June or July.

Neel Kashkari, the president of the Federal Reserve Bank of Minneapolis, even suggested this week that if price increases get stuck, it may make sense to leave interest rates at the current high level all year. While Mr. Kashkari does not vote on policy in 2024, he does have a seat around the discussion table at rate-setting meetings.

“If we continue to see inflation moving sideways, then that would make me question whether we need to do those rate cuts at all,” Mr. Kashkari said during an interview with Pensions & Investments, noting that the economy has a “lot of momentum.”

The average workweek got slightly longer, and now sits at 34.4 hours, the same as it was in March of last year. At the end of 2023, the shrinking workweek had been starting to look like labor demand was weakening even as hiring remained stable.

Stocks are still up in premarket trading, though by less than before the data was released. The 10-year Treasury yield is rising as investors appeared to interpret the jobs data as a confirmation that the Fed won’t rush to cut rates.

The strength of the labor market and stubborn inflation is likely to support the Fed’s “cautious approach to monetary easing,” said Joe Gaffoglio, president of Mutual of America Capital Management.

The Black unemployment rate rose 0.8 percentage points to 6.4 percent, the highest since August 2022. The monthly numbers can bounce around, but the big jump is certainly concerning.

In a landmark, the leisure and hospitality industry returned to its employment level in February 2020, and now sits at about 16.9 million jobs.

The other big sectors powering the gains, as has been common in recent months, were health care at 72,000 jobs and government at 71,000. Construction continued its surprising strength, adding 39,000.

This is starting to look like not a slowdown. Last month’s gain is now substantially above the previous 12-month average of 231,000 jobs.

The household survey, which had been showing much weaker job gains (and even outright losses) in recent months, was much stronger in March. Nearly half a million more people were employed last month, according to that survey.

After some wild revisions in the last few months, they were relatively tame this month, adding a collective 22,000 jobs over January and February.

U.S. employers added 303,000 jobs in March, and the unemployment rate ticked down to 3.8 percent.

Stocks are nudging up in premarket trading as investors await the jobs data. Futures for the S&P 500 are up 0.3 percent, and up 0.4 percent for the tech-heavy Nasdaq Composite.

Beyond jobs, economic data continues to look rosy.

It isn’t just the job market that has been exceeding expectations. Pretty much the whole economy keeps doing the same.

Forecasters went into last year expecting a recession. Instead, the economy gained momentum, ending the year with back-to-back quarters of unusually strong growth in gross domestic product. Revised data released last week showed that G.D.P. growth in the fourth quarter was stronger than initially reported, and that an alternative measure of economic output — which had been telling a more pessimistic story — accelerated at the end of the year.

This year has started out on a similar note. Consumer spending slumped in January but roared back in February . Income growth has been strong as well. And sectors of the economy that struggled last year amid high interest rates, like manufacturing and housing, have recently shown signs of life.

A model from the Federal Reserve Bank of Atlanta estimates that overall economic output grew at a 2.5 percent annual rate in the first quarter — a slowdown from the end of 2023, but still a long way from a recession.

“We’re still plowing along,” said Sarah House, senior economist for Wells Fargo. “Things are hanging in, if not even looking a little bit firmer.”

There has been one important shift: Inflation, which eased steadily for most of last year, has looked more stubborn recently, rising faster on a month-to-month basis in January and February than in late 2023. That will probably lead the Federal Reserve to delay cutting interest rates until the summer, if not later, and has given new life to fears that inflation has not been fully tamed.

At the same time, there are hints that parts of the economy might be weaker than headline figures suggest. Consumers have been pulling back spending on discretionary items, and more borrowers have been falling behind on credit card payments and auto loans — signs that some Americans may be feeling the pinch of continued high prices and interest rates.

“You certainly have a portion of households that are really feeling these higher rates, and it’s affecting how much they can spend,” Ms. House said.

Jordyn Holman and Jeanna Smialek

Will A.I. boost workers’ productivity?

Wendy’s menu boards. Ben & Jerry’s grocery store freezers. Abercrombie & Fitch’s marketing. Many mainstays of the American customer experience are increasingly powered by artificial intelligence.

The question is whether the technology will actually make companies more efficient.

Rapid productivity improvement is the dream for both companies and economic policymakers. If output per hour holds steady, firms must either sacrifice profits or raise prices to pay for wage increases or investment projects. But when firms figure out how to produce more per working hour, it means that they can maintain or expand profits even as they pay or invest more. Economies experiencing productivity booms can experience rapid wage gains and quick growth without as much risk of rapid inflation.

But many economists and officials seem dubious that A.I. — especially generative A.I., which is still in its infancy — has spread enough to show up in productivity data already.

Immigration is helping to meet hiring demand, and may explain data mysteries.

Immigration has been robust over the past two years, creating a flood of potential workers that is both supercharging the job market and leading to surprises and quirks in closely watched economic data.

The Congressional Budget Office estimates that net immigration will total about 3.3 million people this year, matching the 2023 number and far exceeding the 900,000 that was normal before the pandemic.

The jump has come as legal migration and border apprehensions surge, and while the jump in immigration is politically contentious , the resulting pop in population is also fueling strong hiring.

But because immigration flows are uncertain, estimates of that “break even” employment level vary widely. Goldman Sachs puts it at 125,000, while economists at Morgan Stanley think it could be as high as 265,000.

And immigration may help to explain a recent data mystery: a big gap between two primary employment measures.

Each month, the government releases employment figures based on two surveys. The “establishment survey,” compiling data from businesses and government agencies, is used to measure overall job gains. A second measure, drawing on surveys of households and Census Bureau population estimates, is the basis for the unemployment rate and for most demographic information.

Hiring has surged in recent months in the establishment survey even as the household survey has shown it falling. Such a huge divergence is unusual, and it has left analysts scrambling to figure out which survey is giving a reliable read.

Immigration could be behind at least some of the divide. Companies typically report hiring workers of all types, including immigrants, in real time. That explains the strong job gains in the establishment survey. Census estimates, on the other hand, are likely to pick up the recent surge in immigration only with a delay.

For the household survey, “the immigration data that feed into the estimate lag by a year and a half,” Morgan Stanley economists wrote. “In contrast, we think the payroll survey is probably closer to correct.”

How the Fed learned to stop worrying and love strong job gains.

But instead of viewing rapid job gains as a potentially inflationary problem, the Fed has learned to embrace the increase.

That is because recent strong hiring has come alongside a marked pickup in labor supply. Immigration has been much stronger than expected, and millennial men and women in particular are trickling into the labor force, enabling companies to hire without having to compete too fiercely for employees. Wage growth has been strong but not gangbusters, and inflation has cooled across a range of purchases, including those in service categories that are typically sensitive to labor costs.

In fact, the surprising jump in worker supply is a big reason that the central bank might pull off a “soft landing,” in which it sets the labor market down gently and without causing a painful recession.

Mr. Powell has greeted the development as good news. He said this week that the Fed would not rule out further supply improvements, and he noted that immigration was a big reason that the economy blew through forecasters’ expectations for growth last year without generating inflation.