what is the meaning of tabular data presentation

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• Organisational Behaviour
• Human Resource Management
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• 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

What is Tabulation?

The systematic presentation of numerical data in rows and columns is known as Tabulation . It is designed to make presentation simpler and analysis easier. This type of presentation facilitates comparison by putting relevant information close to one another, and it helps in further statistical analysis and interpretation. One of the most important devices for presenting the data in a condensed and readily comprehensible form is tabulation. It aims to provide as much information as possible in the minimum possible space while maintaining the quality and usefulness of the data.

“Tabulation involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration.” – L.R. Connor

Objectives of Tabulation

The aim of tabulation is to summarise a large amount of numerical information into the simplest form. The following are the main objectives of tabulation:

• To make complex data simpler: The main aim of tabulation is to present the classified data in a systematic way. The purpose is to condense the bulk of information (data) under investigation into a simple and meaningful form.
• To save space: Tabulation tries to save space by condensing data in a meaningful form while maintaining the quality and quantity of the data.
• To facilitate comparison: It also aims to facilitate quick comparison of various observations by providing the data in a tabular form.
• To facilitate statistical analysis: Tabulation aims to facilitate statistical analysis because it is the stage between data classification and data presentation. Various statistical measures, including averages, dispersion, correlation, and others, are easily calculated from data that has been systematically tabulated.
• To provide a reference: Since data may be easily identifiable and used when organised in tables with titles and table numbers, tabulation aims to provide a reference for future studies.

Features of a Good Table

Tabulation is a very specialised job. It requires a thorough knowledge of statistical methods, as well as abilities, experience, and common sense. A good table must have the following characteristics:

• Title: The top of the table must have a title and it needs to be very appealing and attractive.
• Manageable Size: The table shouldn’t be too big or too small. The size of the table should be in accordance with its objectives and the characteristics of the data. It should completely cover all significant characteristics of data.
• Attractive: A table should have an appealing appearance that appeals to both the sight and the mind so that the reader can grasp it easily without any strain.
• Special Emphasis: The data to be compared should be placed in the left-hand corner of columns, with their titles in bold letters.
• Fit with the Objective: The table should reflect the objective of the statistical investigation.
• Simplicity: To make the table easily understandable, it should be simple and compact.
• Data Comparison: The data to be compared must be placed closely in the columns.
• Numbered Columns and Rows: When there are several rows and columns in a table, they must be numbered for reference.
• Clarity: A table should be prepared so that even a layman may make conclusions from it. The table should contain all necessary information and it must be self-explanatory.
• Units: The unit designations should be written on the top of the table, below the title. For example, Height in cm, Weight in kg, Price in ₹, etc. However, if different items have different units, then they should be mentioned in the respective rows and columns.
• Suitably Approximated: If the figures are large, then they should be rounded or approximated.
• Scientifically Prepared: The preparation of the table should be done in a systematic and logical manner and should be free from any kind of ambiguity and overlapping. 

Components of a Table

A table’s preparation is an art that requires skilled data handling. It’s crucial to understand the components of a good statistical table before constructing one. A table is created when all of these components are put together in a systematic order. In simple terms, a good table should include the following components:

1. Table Number:

Each table needs to have a number so it may be quickly identified and used as a reference.

• If there are many tables, they should be numbered in a logical order.
• The table number can be given at the top of the table or the beginning of the table title.
• The table is also identified by its location using subscripted numbers like 1.2, 2.1, etc. For instance, Table Number 3.1 should be seen as the first table of the third chapter.

Each table should have a suitable title. A table’s contents are briefly described in the title.

• The title should be simple, self-explanatory, and free from ambiguity.
• A title should be brief and presented clearly, usually below the table number.
• In certain cases, a long title is preferable for clarification. In these cases, a ‘Catch Title’ may be placed above the ‘Main Title’. For instance , the table’s contents might come after the firm’s name, which appears as a catch title.
• Contents of Title: The title should include the following information:  (i) Nature of data, or classification criteria (ii) Subject-matter (iii) Place to which the data relates  (iv) Time to which the data relates  (v) Source to which the data belongs  (vi) Reference to the data, if available.

3. Captions or Column Headings:

A column designation is given to explain the figures in the column at the top of each column in a table. This is referred to as a “Column heading” or “Caption”.

• Captions are used to describe the names or heads of vertical columns.
• To save space, captions are generally placed in small letters in the middle of the columns.

4. Stubs or Row Headings:

Each row of the table needs to have a heading, similar to a caption or column heading. The headers of horizontal rows are referred to as stubs. A brief description of the row headers may also be provided at the table’s left-hand top.

5. Body of Table:

The table’s most crucial component is its body, which contains data (numerical information).

• The location of any one figure or data in the table is fixed and determined by the row and column of the table.
• The columns and rows in the main body’s arrangement of numerical data are arranged from top to bottom.
• The size and shape of the main body should be planned in accordance with the nature of the figures and the purpose of the study.
• As the body of the table summarises the facts and conclusions of the statistical investigation, it must be ensured that the table does not have irrelevant information.

6. Unit of Measurement:

If the unit of measurement of the figures in the table (real data) does not change throughout the table, it should always be provided along with the title.

• However, these units must be mentioned together with stubs or captions if rows or columns have different units.
• If there are large figures, they should be rounded up and the rounding method should be stated.

7. Head Notes:

If the main title does not convey enough information, a head note is included in small brackets in prominent words right below the main title.

• A head-note is included to convey any relevant information.
• For instance, the table frequently uses the units of measurement “in million rupees,” “in tonnes,” “in kilometres,” etc. Head notes are also known as Prefatory Notes .

8. Source Note:

A source note refers to the place where information was obtained.

• In the case of secondary data, a source note is provided.
• Name of the book, page number, table number, etc., from which the data were collected should all be included in the source. If there are multiple sources, each one must be listed in the source note.
• If a reader wants to refer to the original data, the source note enables him to locate the data. Usually, the source note appears at the bottom of the table. For example, the source note may be: ‘Census of India, 2011’.
• Importance: A source note is useful for three reasons: -> It provides credit to the source (person or group), who collected the data; -> It provides a reference to source material that may be more complete; -> It offers some insight into the reliability of the information and its source.

9. Footnotes:

The footnote is the last part of the table. The unique characteristic of the data content of the table that is not self-explanatory and has not previously been explained is mentioned in the footnote.

• Footnotes are used to provide additional information that is not provided by the heading, title, stubs, caption, etc.
• When there are many footnotes, they are numbered in order.
• Footnotes are identified by the symbols *, @, £, etc.
• In general, footnotes are used for the following reasons: (i) To highlight any exceptions to the data (ii)Any special circumstances affecting the data; and (iii)To clarify any information in the data.

Merits of Tabular Presentation of Data

The following are the merits of tabular presentation of data:

• Brief and Simple Presentation: Tabular presentation is possibly the simplest method of data presentation. As a result, information is simple to understand. A significant amount of statistical data is also presented in a very brief manner.
• Facilitates Comparison: By grouping the data into different classes, tabulation facilitates data comparison.
• Simple Analysis: Analysing data from tables is quite simple. One can determine the data’s central tendency, dispersion, and correlation by organising the data as a table.
• Highlights Characteristics of the Data:  Tabulation highlights characteristics of the data. As a result of this, it is simple to remember the statistical facts.
• Cost-effective: Tabular presentation is a very cost-effective way to convey data. It saves time and space.
• Provides Reference: As the data provided in a tabular presentation can be used for other studies and research, it acts as a source of reference.

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Data presentation: A comprehensive guide

Learn how to create data presentation effectively and communicate your insights in a way that is clear, concise, and engaging.

Raja Bothra

Building presentations

Hey there, fellow data enthusiast!

Welcome to our comprehensive guide on data presentation.

Whether you're an experienced presenter or just starting, this guide will help you present your data like a pro.

We'll dive deep into what data presentation is, why it's crucial, and how to master it. So, let's embark on this data-driven journey together.

What is data presentation?

Data presentation is the art of transforming raw data into a visual format that's easy to understand and interpret. It's like turning numbers and statistics into a captivating story that your audience can quickly grasp. When done right, data presentation can be a game-changer, enabling you to convey complex information effectively.

Why are data presentations important?

Imagine drowning in a sea of numbers and figures. That's how your audience might feel without proper data presentation. Here's why it's essential:

• Clarity : Data presentations make complex information clear and concise.
• Engagement : Visuals, such as charts and graphs, grab your audience's attention.
• Comprehension : Visual data is easier to understand than long, numerical reports.
• Decision-making : Well-presented data aids informed decision-making.
• Impact : It leaves a lasting impression on your audience.

Types of data presentation

Now, let's delve into the diverse array of data presentation methods, each with its own unique strengths and applications. We have three primary types of data presentation, and within these categories, numerous specific visualization techniques can be employed to effectively convey your data.

1. Textual presentation

Textual presentation harnesses the power of words and sentences to elucidate and contextualize your data. This method is commonly used to provide a narrative framework for the data, offering explanations, insights, and the broader implications of your findings. It serves as a foundation for a deeper understanding of the data's significance.

2. Tabular presentation

Tabular presentation employs tables to arrange and structure your data systematically. These tables are invaluable for comparing various data groups or illustrating how data evolves over time. They present information in a neat and organized format, facilitating straightforward comparisons and reference points.

3. Graphical presentation

Graphical presentation harnesses the visual impact of charts and graphs to breathe life into your data. Charts and graphs are powerful tools for spotlighting trends, patterns, and relationships hidden within the data. Let's explore some common graphical presentation methods:

• Bar charts: They are ideal for comparing different categories of data. In this method, each category is represented by a distinct bar, and the height of the bar corresponds to the value it represents. Bar charts provide a clear and intuitive way to discern differences between categories.
• Pie charts: It excel at illustrating the relative proportions of different data categories. Each category is depicted as a slice of the pie, with the size of each slice corresponding to the percentage of the total value it represents. Pie charts are particularly effective for showcasing the distribution of data.
• Line graphs: They are the go-to choice when showcasing how data evolves over time. Each point on the line represents a specific value at a particular time period. This method enables viewers to track trends and fluctuations effortlessly, making it perfect for visualizing data with temporal dimensions.
• Scatter plots: They are the tool of choice when exploring the relationship between two variables. In this method, each point on the plot represents a pair of values for the two variables in question. Scatter plots help identify correlations, outliers, and patterns within data pairs.

The selection of the most suitable data presentation method hinges on the specific dataset and the presentation's objectives. For instance, when comparing sales figures of different products, a bar chart shines in its simplicity and clarity. On the other hand, if your aim is to display how a product's sales have changed over time, a line graph provides the ideal visual narrative.

Additionally, it's crucial to factor in your audience's level of familiarity with data presentations. For a technical audience, more intricate visualization methods may be appropriate. However, when presenting to a general audience, opting for straightforward and easily understandable visuals is often the wisest choice.

In the world of data presentation, choosing the right method is akin to selecting the perfect brush for a masterpiece. Each tool has its place, and understanding when and how to use them is key to crafting compelling and insightful presentations. So, consider your data carefully, align your purpose, and paint a vivid picture that resonates with your audience.

What to include in data presentation

When creating your data presentation, remember these key components:

• Data points : Clearly state the data points you're presenting.
• Comparison : Highlight comparisons and trends in your data.
• Graphical methods : Choose the right chart or graph for your data.
• Infographics : Use visuals like infographics to make information more digestible.
• Numerical values : Include numerical values to support your visuals.
• Qualitative information : Explain the significance of the data.
• Source citation : Always cite your data sources.

How to structure an effective data presentation

Creating a well-structured data presentation is not just important; it's the backbone of a successful presentation. Here's a step-by-step guide to help you craft a compelling and organized presentation that captivates your audience:

1. Know your audience

Understanding your audience is paramount. Consider their needs, interests, and existing knowledge about your topic. Tailor your presentation to their level of understanding, ensuring that it resonates with them on a personal level. Relevance is the key.

2. Have a clear message

Every effective data presentation should convey a clear and concise message. Determine what you want your audience to learn or take away from your presentation, and make sure your message is the guiding light throughout your presentation. Ensure that all your data points align with and support this central message.

3. Tell a compelling story

Human beings are naturally wired to remember stories. Incorporate storytelling techniques into your presentation to make your data more relatable and memorable. Your data can be the backbone of a captivating narrative, whether it's about a trend, a problem, or a solution. Take your audience on a journey through your data.

4. Leverage visuals

Visuals are a powerful tool in data presentation. They make complex information accessible and engaging. Utilize charts, graphs, and images to illustrate your points and enhance the visual appeal of your presentation. Visuals should not just be an accessory; they should be an integral part of your storytelling.

5. Be clear and concise

Avoid jargon or technical language that your audience may not comprehend. Use plain language and explain your data points clearly. Remember, clarity is king. Each piece of information should be easy for your audience to digest.

6. Practice your delivery

Practice makes perfect. Rehearse your presentation multiple times before the actual delivery. This will help you deliver it smoothly and confidently, reducing the chances of stumbling over your words or losing track of your message.

A basic structure for an effective data presentation

Armed with a comprehensive comprehension of how to construct a compelling data presentation, you can now utilize this fundamental template for guidance:

In the introduction, initiate your presentation by introducing both yourself and the topic at hand. Clearly articulate your main message or the fundamental concept you intend to communicate.

Moving on to the body of your presentation, organize your data in a coherent and easily understandable sequence. Employ visuals generously to elucidate your points and weave a narrative that enhances the overall story. Ensure that the arrangement of your data aligns with and reinforces your central message.

As you approach the conclusion, succinctly recapitulate your key points and emphasize your core message once more. Conclude by leaving your audience with a distinct and memorable takeaway, ensuring that your presentation has a lasting impact.

Additional tips for enhancing your data presentation

To take your data presentation to the next level, consider these additional tips:

• Consistent design : Maintain a uniform design throughout your presentation. This not only enhances visual appeal but also aids in seamless comprehension.
• High-quality visuals : Ensure that your visuals are of high quality, easy to read, and directly relevant to your topic.
• Concise text : Avoid overwhelming your slides with excessive text. Focus on the most critical points, using visuals to support and elaborate.
• Anticipate questions : Think ahead about the questions your audience might pose. Be prepared with well-thought-out answers to foster productive discussions.

By following these guidelines, you can structure an effective data presentation that not only informs but also engages and inspires your audience. Remember, a well-structured presentation is the bridge that connects your data to your audience's understanding and appreciation.

Do’s and don'ts on a data presentation

• Use visuals : Incorporate charts and graphs to enhance understanding.
• Keep it simple : Avoid clutter and complexity.
• Highlight key points : Emphasize crucial data.
• Engage the audience : Encourage questions and discussions.
• Practice : Rehearse your presentation.

Don'ts:

• Overload with data : Less is often more; don't overwhelm your audience.
• Fit Unrelated data : Stay on topic; don't include irrelevant information.
• Neglect the audience : Ensure your presentation suits your audience's level of expertise.
• Read word-for-word : Avoid reading directly from slides.
• Lose focus : Stick to your presentation's purpose.

Summarizing key takeaways

• Definition : Data presentation is the art of visualizing complex data for better understanding.
• Importance : Data presentations enhance clarity, engage the audience, aid decision-making, and leave a lasting impact.
• Types : Textual, Tabular, and Graphical presentations offer various ways to present data.
• Choosing methods : Select the right method based on data, audience, and purpose.
• Components : Include data points, comparisons, visuals, infographics, numerical values, and source citations.
• Structure : Know your audience, have a clear message, tell a compelling story, use visuals, be concise, and practice.
• Do's and don'ts : Do use visuals, keep it simple, highlight key points, engage the audience, and practice. Don't overload with data, include unrelated information, neglect the audience's expertise, read word-for-word, or lose focus.

1. What is data presentation, and why is it important in 2023?

Data presentation is the process of visually representing data sets to convey information effectively to an audience. In an era where the amount of data generated is vast, visually presenting data using methods such as diagrams, graphs, and charts has become crucial. By simplifying complex data sets, presentation of the data may helps your audience quickly grasp much information without drowning in a sea of chart's, analytics, facts and figures.

2. What are some common methods of data presentation?

There are various methods of data presentation, including graphs and charts, histograms, and cumulative frequency polygons. Each method has its strengths and is often used depending on the type of data you're using and the message you want to convey. For instance, if you want to show data over time, try using a line graph. If you're presenting geographical data, consider to use a heat map.

3. How can I ensure that my data presentation is clear and readable?

To ensure that your data presentation is clear and readable, pay attention to the design and labeling of your charts. Don't forget to label the axes appropriately, as they are critical for understanding the values they represent. Don't fit all the information in one slide or in a single paragraph. Presentation software like Prezent and PowerPoint can help you simplify your vertical axis, charts and tables, making them much easier to understand.

4. What are some common mistakes presenters make when presenting data?

One common mistake is trying to fit too much data into a single chart, which can distort the information and confuse the audience. Another mistake is not considering the needs of the audience. Remember that your audience won't have the same level of familiarity with the data as you do, so it's essential to present the data effectively and respond to questions during a Q&A session.

5. How can I use data visualization to present important data effectively on platforms like LinkedIn?

When presenting data on platforms like LinkedIn, consider using eye-catching visuals like bar graphs or charts. Use concise captions and e.g., examples to highlight the single most important information in your data report. Visuals, such as graphs and tables, can help you stand out in the sea of textual content, making your data presentation more engaging and shareable among your LinkedIn connections.

Create your data presentation with prezent

Prezent can be a valuable tool for creating data presentations. Here's how Prezent can help you in this regard:

• Time savings : Prezent saves up to 70% of presentation creation time, allowing you to focus on data analysis and insights.
• On-brand consistency : Ensure 100% brand alignment with Prezent's brand-approved designs for professional-looking data presentations.
• Effortless collaboration : Real-time sharing and collaboration features make it easy for teams to work together on data presentations.
• Data storytelling : Choose from 50+ storylines to effectively communicate data insights and engage your audience.
• Personalization : Create tailored data presentations that resonate with your audience's preferences, enhancing the impact of your data.

In summary, Prezent streamlines the process of creating data presentations by offering time-saving features, ensuring brand consistency, promoting collaboration, and providing tools for effective data storytelling. Whether you need to present data to clients, stakeholders, or within your organization, Prezent can significantly enhance your presentation-making process.

So, go ahead, present your data with confidence, and watch your audience be wowed by your expertise.

Thank you for joining us on this data-driven journey. Stay tuned for more insights, and remember, data presentation is your ticket to making numbers come alive!

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1.3: Presentation of Data

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Learning Objectives

• To learn two ways that data will be presented in the text.

In this book we will use two formats for presenting data sets. The first is a data list, which is an explicit listing of all the individual measurements, either as a display with space between the individual measurements, or in set notation with individual measurements separated by commas.

Example \(\PageIndex{1}\)

The data obtained by measuring the age of \(21\) randomly selected students enrolled in freshman courses at a university could be presented as the data list:

\[\begin{array}{cccccccccc}18 & 18 & 19 & 19 & 19 & 18 & 22 & 20 & 18 & 18 & 17 \\ 19 & 18 & 24 & 18 & 20 & 18 & 21 & 20 & 17 & 19 &\end{array} \nonumber \]

or in set notation as:

\[ \{18,18,19,19,19,18,22,20,18,18,17,19,18,24,18,20,18,21,20,17,19\} \nonumber \]

A data set can also be presented by means of a data frequency table, a table in which each distinct value \(x\) is listed in the first row and its frequency \(f\), which is the number of times the value \(x\) appears in the data set, is listed below it in the second row.

Example \(\PageIndex{2}\)

The data set of the previous example is represented by the data frequency table

\[\begin{array}{c|cccccc}x & 17 & 18 & 19 & 20 & 21 & 22 & 24 \\ \hline f & 2 & 8 & 5 & 3 & 1 & 1 & 1\end{array} \nonumber \]

The data frequency table is especially convenient when data sets are large and the number of distinct values is not too large.

Key Takeaway

• Data sets can be presented either by listing all the elements or by giving a table of values and frequencies.

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Data Presentation - Tables

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Tables are a useful way to organize information using rows and columns. Tables are a versatile organization tool and can be used to communicate information on their own, or they can be used to accompany another data representation type (like a graph). Tables support a variety of parameters and can be used to keep track of frequencies, variable associations, and more.

For example, given below are the weights of 20 students in grade 10: \[50, 45, 48, 39, 40, 48, 54, 50, 48, 48, \\ 50, 39, 41, 46, 44, 43, 54, 57, 60, 45.\]

To find the frequency of \(48\) in this data, count the number of times that \(48\) appears in the list. There are \(4\) students that have this weight.

The list above has information about the weight of \(20\) students, and since the data has been arranged haphazardly, it is difficult to classify the students properly.

To make the information more clear, tabulate the given data.

\[\begin{array} \\ \text{Weights in kg} & & & \text{Frequency} \\ 39 & & & 2 \\ 40 & & & 1 \\ 41 & & & 1 \\ 43 & & & 1 \\ 44 & & & 1 \\ 45 & & & 2 \\ 46 & & & 1 \\ 48 & & & 4 \\ 50 & & & 3 \\ 54 & & & 2 \\ 57 & & & 1 \\ 60 & & & 1 \end{array}\]

This table makes the data more easy to understand.

Making a Table

Making and using tables.

To make a table, first decide how many rows and columns are needed to clearly display the data. To do this, consider how many variables are included in the data set.

The following is an example of a table where there are two variables.

The following is an example of a table with three variables.

A table is good for organizing quantitative data in a way that it is easy to look things up. For example, a table would be good way to associate a person’s name, age, and favorite food. However, when trying to communicate relations, such as how a person’s favorite food changes over time, a graph would be a better choice.

Using the table below, determine the average age of the group?

Good practices for making tables Label what each row or column represents Include units in labels when data is numerical Format data consistently (use consistent units and formatting)

What is wrong with this table? Flavor of Ice Cream Number Sold (cones) Chocolate 104 Vanilla two-hundred Strawberry 143 Coconut thirty Mango 126 Show answer Answer: The data isn’t consistently formatted. The number of cones sold is written in numbers in both symbols and words. It would be easier to understand if all entries were numerical symbols.

What is wrong with this table? Jack blue Sarah yellow Billy green Ron red Christina blue Margret purple Show answer Answer: There are no labels on the columns. It is not clear what the table is displaying — does the table show what color shirt each person is wearing? Do it show what each person's favorite color is? It isn't clear because labels are missing.

Many word processing softwares include tools for making tables. You can easily make tables in Microsoft Word and Excel and in Google Docs and Sheets.

Here is an example table (left blank) with which you could record information about a person's age, weight, and height.

Tables are used to present information in all types of fields. Geologists might make a table to record data about types of rocks they find while doing field work, political researchers might create a table to record information about potential voters, and physicists might make a table to record observations about the speed of a ball rolled on various surfaces.

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Statistics Made Easy

What is Tabular Data? (Definition & Example)

In statistics, tabular data refers to data that is organized in a table with rows and columns.

Within the table, the rows represent observations and the columns represent attributes for those observations.

For example, the following table represents tabular data:

This dataset has 9 rows and 5 columns.

Each row represents one basketball player and the five columns describe different attributes about the player including:

• Player name
• Minutes played

The opposite of tabular data would be visual data , which would be some type of plot or chart that helps us visualize the values in a dataset.

For example, we might have the following bar chart that helps us visualize the total minutes played by each player in the dataset:

This would be an example of visual data .

It contains the exact same information about player names and minutes played for the players in the dataset, but it’s simply displayed in a visual form instead of a tabular form.

Or we might have the following scatterplot that helps us visualize the relationship between minutes played and points scored for each player:

This is another example of visual data .

When is Tabular Data Used in Practice?

In practice, tabular data is the most common type of data that you’ll run across in the real world.

In the real world, most data that is saved in an Excel spreadsheet is considered tabular data because the rows represent observations and the columns represent attributes for those observations.

For example, here’s what our basketball dataset from earlier might look like in an Excel spreadsheet:

This format is one of the most natural ways to collect and store values in a dataset, which is why it’s used so often.

Additional Resources

The following tutorials explain other common terms in statistics:

Why is Statistics Important? Why is Sample Size Important in Statistics? What is an Observation in Statistics? What is Considered Raw Data in Statistics?

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4   Introduction to Tabular Data

An email inbox is a list of messages. For each message, your inbox stores a bunch of information: its sender, the subject line, the conversation it’s part of, the body, and quite a bit more.

A music playlist. For each song, your music player maintains a bunch of information: its name, the singer, its length, its genre, and so on.

A filesystem folder or directory. For each file, your filesystem records a name, a modification date, size, and other information.

Do Now! Can you come up with more examples?

Responses to a party invitation.

A gradebook.

A calendar agenda.

They consists of rows and columns. For instance, each song or email message or file is a row. Each of their characteristics— the song title, the message subject, the filename— is a column.

Each row has the same columns as the other rows, in the same order.

A given column has the same type, but different columns can have different types. For instance, an email message has a sender’s name, which is a string; a subject line, which is a string; a sent date, which is a date; whether it’s been read, which is a Boolean; and so on.

The rows are usually in some particular order. For instance, the emails are ordered by which was most recently sent.

Exercise Find the characteristics of tabular data in the other examples described above, as well as in the ones you described.

We will now learn how to program with tables and to think about decomposing tasks involving them. You can also look up the full Pyret documentation for table operations .

4.1   Creating Tabular Data

table: name, age row: "Alice", 30 row: "Bob", 40 row: "Carol", 25 end

Exercise Change different parts of the above example— e.g., remove a necessary value from a row, add an extraneous one, remove a comma, add an extra comma, leave an extra comma at the end of a row— and see what errors you get.

check: table: name, age row: "Alice", 30 row: "Bob", 40 row: "Carol", 25 end is-not table: age, name row: 30, "Alice" row: 40, "Bob" row: 25, "Carol" end end

people = table: name, age row: "Alice", 30 row: "Bob", 40 row: "Carol", 25 end

create the sheet on your own,

create a sheet collaboratively with friends,

find data on the Web that you can import into a sheet,

create a Google Form that you get others to fill out, and obtain a sheet out of their responses

4.2   Processing Rows

Let’s now learn how we can actually process a table. Pyret offers a variety of built-in operations that make it quite easy to perform interesting computations over tables. In addition, as we will see later [REF], if we don’t find these sufficient, we can write our own. For now, we’ll focus on the operations Pyret provides.

Which emails were sent by a particular user?

Which songs were sung by a particular artist?

Which are the most frequently played songs in a playlist?

Which are the least frequently played songs in a playlist?

4.2.1   Keeping

email = table: sender, recipient, subject row: 'Matthias Felleisen', 'Pedro Diaz', 'Introduction' row: 'Joe Politz', 'Pedro Diaz', 'Class on Friday' row: 'Matthias Felleisen', 'Pedro Diaz', 'Book comments' row: 'Mia Minnes', 'Pedro Diaz', 'CSE8A Midterm' end

sieve email using sender: sender == 'Matthias Felleisen' end

sieve playlist using artist: (artist == 'Deep Purple') or (artist == 'Van Halen') end

Exercise Write a table for to use as playlist that works with the sieve expression above.

Exercise Write a sieve expression on the email table above that would result in a table with zero rows.

4.2.2   Ordering

order playlist: play-count ascending end

Note that what goes between the : and end is not an expression. Therefore, we cannot write arbitrary code here. We can only name columns and indicate which way they should be ordered.

4.2.3   Combining Keeping and Ordering

Of the emails from a particular person, which is the oldest?

Of the songs by a particular artist, which have we played the least often?

Do Now! Take a moment to think about how you would write these with what you have seen so far.

mf-emails = sieve email using sender: sender == 'Matthias Felleisen' end order mf-emails: sent-date ascending end

Exercise Write the second example as a composition of keep and order operations on a playlist table.

4.2.4   Extending

extend employees using hourly-wage, hours-worked: total-wage: hourly-wage * hours-worked end

ext-email = extend email using subject: subject-length: string-length(subject) end order ext-email: subject-length descending end

4.2.5   Transforming, Cleansing, and Normalizing

There are times when a table is “almost right”, but requires a little adjusting. For instance, we might have a table of customer requests for a free sample, and want to limit each customer to at most a certain number. We might get temperature readings from different countries in different formats, and want to convert them all to one single format. Because unit errors can be dangerous ! We might have a gradebook where different graders have used different levels of precision, and want to standardize all of them to have the same level of precision.

transform orders using count: count: num-min(count, 3) end

transform gradebook using total-grade: total-grade: num-round(total-grade) end

transform weather using temp, unit: temp: if unit == "F": fahrenheit-to-celsius(temp) else: temp end unit: if unit == "F": "C" else: unit end end

Do Now! In this example, why do we also transform unit ?

4.2.6   Selecting

select name, total-grade from gradebook end

ss = select artist, song from playlist end order ss: artist ascending end

4.2.7   Summary of Row-Wise Table Operations

We’ve seen a lot in a short span. Specifically, we have seen several operations that consume a table and produce a new one according to some criterion. It’s worth summarizing the impact each of them has in terms of key table properties (where “-” means the entry is left unchanged):

The italicized entries reflect how the new table may differ from the old. Note that an entry like “reduced” or “altered” should be read as potentially reduced or altered; depending on the specific operation and the content of the table, there may be no change at all. (For instance, if a table is already sorted according to the criterion given in an order expression, the row order will not change.) However, in general one should expect the kind of change described in the above grid.

Observe that both dimensions of this grid provide interesting information. Unsurprisingly, each row has at least some kind of impact on a table (otherwise the operation would be useless and would not exist). Likewise, each column also has at least one way of impacting it. Furthermore, observe that most entries leave the table unchanged: that means each operation has limited impact on the table, careful to not overstep the bounds of its mandate.

On the one hand, the decision to limit the impact of each operation means that to achieve complex tasks, we may have to compose several operations together. We have already seen examples of this earlier this chapter. However, there is also a much more subtle consequence: it also means that to achieve complex tasks, we can compose several operations and get exactly what we want. If we had fewer operations that each did more, then composing them might have various undesired or (worse) unintended consequences, making it very difficult for us to obtain exactly the answer we want. Instead, the operations above follow the principle of orthogonality : no operation shadows what any other operation does, so they can be composed freely.

As a result of having these operations, we can think of tables also algebrically. Concretely, when given a problem, we should again begin with concrete examples of what we’re starting with and where we want to end. Then we can ask ourselves questions like, “Does the number of columns stay the same, grow, or shrink?”, “Does the number of rows stay the same or shrink?”, and so on. The grid above now provides us a toolkit by which we can start to decompose the task into individual operations. Of course, we still have to think: the order of operations matters, and sometimes we have to perform an operation mutiple times. Still, this grid is a useful guide to hint us towards the operations that might help solve our problem.

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• Korean J Anesthesiol
• v.70(3); 2017 Jun

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.

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• Presentation of Data

Data Presenting for Clearer Reference

Imagine the statistical data without a definite presentation, will be burdensome! Data presentation is one of the important aspects of Statistics. Presenting the data helps the users to study and explain the statistics thoroughly. We are going to discuss this presentation of data and know-how information is laid down methodically. 

In this context, we are going to present the topic - Presentation of Data which is to be referred to by the students and the same is to be studied in regard to the types of presentations of data. 

Presentation of Data and Information

Statistics is all about data. Presenting data effectively and efficiently is an art. You may have uncovered many truths that are complex and need long explanations while writing. This is where the importance of the presentation of data comes in. You have to present your findings in such a way that the readers can go through them quickly and understand each and every point that you wanted to showcase. As time progressed and new and complex research started happening, people realized the importance of the presentation of data to make sense of the findings.

Define Data Presentation

Data presentation is defined as the process of using various graphical formats to visually represent the relationship between two or more data sets so that an informed decision can be made based on them.

Types of Data Presentation

Broadly speaking, there are three methods of data presentation:

Diagrammatic

Textual Ways of Presenting Data

Out of the different methods of data presentation, this is the simplest one. You just write your findings in a coherent manner and your job is done. The demerit of this method is that one has to read the whole text to get a clear picture. Yes, the introduction, summary, and conclusion can help condense the information.

Tabular Ways of Data Presentation and Analysis

To avoid the complexities involved in the textual way of data presentation, people use tables and charts to present data. In this method, data is presented in rows and columns - just like you see in a cricket match showing who made how many runs. Each row and column have an attribute (name, year, sex, age, and other things like these). It is against these attributes that data is written within a cell.

Diagrammatic Presentation: Graphical Presentation of Data in Statistics

This kind of data presentation and analysis method says a lot with dramatically short amounts of time.

Diagrammatic Presentation has been divided into further categories:

Geometric Diagram

When a Diagrammatic presentation involves shapes like a bar or circle, we call that a Geometric Diagram. Examples of Geometric Diagram

Bar Diagram

Simple Bar Diagram

Simple Bar Diagram is composed of rectangular bars. All of these bars have the same width and are placed at an equal distance from each other. The bars are placed on the X-axis. The height or length of the bars is used as the means of measurement. So, on the Y-axis, you have the measurement relevant to the data. 

Suppose, you want to present the run scored by each batsman in a game in the form of a bar chart. Mark the runs on the Y-axis - in ascending order from the bottom. So, the lowest scorer will be represented in the form of the smallest bar and the highest scorer in the form of the longest bar.

Multiple Bar Diagram

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In many states of India, electric bills have bar diagrams showing the consumption in the last 5 months. Along with these bars, they also have bars that show the consumption that happened in the same months of the previous year. This kind of Bar Diagram is called Multiple Bar Diagrams.

Component Bar Diagram

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Sometimes, a bar is divided into two or more parts. For example, if there is a Bar Diagram, the bars of which show the percentage of male voters who voted and who didn’t and the female voters who voted and who didn’t. Instead of creating separate bars for who did and who did not, you can divide one bar into who did and who did not.

A pie chart is a chart where you divide a pie (a circle) into different parts based on the data. Each of the data is first transformed into a percentage and then that percentage figure is multiplied by 3.6 degrees. The result that you get is the angular degree of that corresponding data to be drawn in the pie chart. So, for example, you get 30 degrees as the result, on the pie chart you draw that angle from the center.

Frequency Diagram

Suppose you want to present data that shows how many students have 1 to 2 pens, how many have 3 to 5 pens, how many have 6 to 10 pens (grouped frequency) you do that with the help of a Frequency Diagram. A Frequency Diagram can be of many kinds:

Where the grouped frequency of pens (from the above example) is written on the X-axis and the numbers of students are marked on the Y-axis. The data is presented in the form of bars.

Frequency Polygon

When you join the midpoints of the upper side of the rectangles in a histogram, you get a Frequency Polygon

Frequency Curve

When you draw a freehand line that passes through the points of the Frequency Polygon, you get a Frequency Curve.

Ogive 

Suppose 2 students got 0-20 marks in maths, 5 students got 20-30 marks and 4 students got 30-50 marks in Maths. So how many students got less than 50 marks? Yes, 5+2=7. And how many students got more than 20 marks? 5+4=9. This type of more than and less than data are represented in the form of the ogive. The meeting point of the less than and more than line will give you the Median.

Arithmetic Line Graph

If you want to see the trend of Corona infection vs the number of recoveries from January 2020 to December 2020, you can do that in the form of an Arithmetic Line Graph. The months should be marked on the X-axis and the number of infections and recoveries are marked on the Y-axis. You can compare if the recovery is greater than the infection and if the recovery and infection are going at the same rate or not with the help of this Diagram.

Did You Know?

Sir Ronald Aylmer Fisher is known as the father of modern statistics.

FAQs on Presentation of Data

1. What are the 4 types of Tabular Presentation?

The tabular presentation method can be further divided into 4 categories:

Qualitative

Quantitative

Qualitative classification is done when the attributes in the table are some kind of ‘quality’ or feature. Suppose you want to make a table where you would show how many batsmen made half-centuries and how many batsmen made centuries in IPL 2020. Notice that the data would have only numbers - no age, sex, height is needed. This type of tabulation is called quantitative tabulation.

If you want to make a table that would inform which year’s world cup, which team won. The classifying variable, here, is year or time. This kind of classification is called Temporal classification.

If you want to list the top 5 coldest places in the world. The classifying variable here would be a place in each case. This kind of classification is called Spatial Classification.

2. Are bar charts and histograms the Same?

No, they are not the same. With a histogram, you measure the frequency of quantitative data. With bar charts, you compare categorical data.

3. What is the definition of Data Presentation?

When research work is completed, the data gathered from it can be quite large and complex. Organizing the data in a coherent, easy-to-understand, quick to read and graphical way is called data presentation.

What is Tabular Data? (Definition & Example)

In statistics, tabular data refers to data that is organized in a table with rows and columns.

Within the table, the rows represent observations and the columns represent attributes for those observations.

For example, the following table represents tabular data:

This dataset has 9 rows and 5 columns.

Each row represents one basketball player and the five columns describe different attributes about the player including:

• Player name
• Minutes played

The opposite of tabular data would be visual data , which would be some type of plot or chart that helps us visualize the values in a dataset.

For example, we might have the following bar chart that helps us visualize the total minutes played by each player in the dataset:

This would be an example of visual data .

It contains the exact same information about player names and minutes played for the players in the dataset, but it’s simply displayed in a visual form instead of a tabular form.

Or we might have the following scatterplot that helps us visualize the relationship between minutes played and points scored for each player:

This is another example of visual data .

When is Tabular Data Used in Practice?

In practice, tabular data is the most common type of data that you’ll run across in the real world.

In the real world, most data that is saved in an Excel spreadsheet is considered tabular data because the rows represent observations and the columns represent attributes for those observations.

For example, here’s what our basketball dataset from earlier might look like in an Excel spreadsheet:

This format is one of the most natural ways to collect and store values in a dataset, which is why it’s used so often.

Additional Resources

The following tutorials explain other common terms in statistics:

Why is Statistics Important? Why is Sample Size Important in Statistics? What is an Observation in Statistics? What is Considered Raw Data in Statistics?

How to Write a Nested IFERROR Statement in Excel

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Presentation of Data

Statistics deals with the collection, presentation and analysis of the data, as well as drawing meaningful conclusions from the given data. Generally, the data can be classified into two different types, namely primary data and secondary data. If the information is collected by the investigator with a definite objective in their mind, then the data obtained is called the primary data. If the information is gathered from a source, which already had the information stored, then the data obtained is called secondary data. Once the data is collected, the presentation of data plays a major role in concluding the result. Here, we will discuss how to present the data with many solved examples.

What is Meant by Presentation of Data?

As soon as the data collection is over, the investigator needs to find a way of presenting the data in a meaningful, efficient and easily understood way to identify the main features of the data at a glance using a suitable presentation method. Generally, the data in the statistics can be presented in three different forms, such as textual method, tabular method and graphical method.

Presentation of Data Examples

Now, let us discuss how to present the data in a meaningful way with the help of examples.

Consider the marks given below, which are obtained by 10 students in Mathematics:

36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

Find the range for the given data.

Given Data: 36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

The data given is called the raw data.

First, arrange the data in the ascending order : 25, 36, 42, 55, 60, 62, 73, 75, 78, 95.

Therefore, the lowest mark is 25 and the highest mark is 95.

We know that the range of the data is the difference between the highest and the lowest value in the dataset.

Therefore, Range = 95-25 = 70.

Note: Presentation of data in ascending or descending order can be time-consuming if we have a larger number of observations in an experiment.

Now, let us discuss how to present the data if we have a comparatively more number of observations in an experiment.

Consider the marks obtained by 30 students in Mathematics subject (out of 100 marks)

10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88.

In this example, the number of observations is larger compared to example 1. So, the presentation of data in ascending or descending order is a bit time-consuming. Hence, we can go for the method called ungrouped frequency distribution table or simply frequency distribution table . In this method, we can arrange the data in tabular form in terms of frequency.

For example, 3 students scored 50 marks. Hence, the frequency of 50 marks is 3. Now, let us construct the frequency distribution table for the given data.

Therefore, the presentation of data is given as below:

The following example shows the presentation of data for the larger number of observations in an experiment.

Consider the marks obtained by 100 students in a Mathematics subject (out of 100 marks)

95, 67, 28, 32, 65, 65, 69, 33, 98, 96,76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62, 37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90, 44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75, 66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36.

Now, we have 100 observations to present the data. In this case, we have more data when compared to example 1 and example 2. So, these data can be arranged in the tabular form called the grouped frequency table. Hence, we group the given data like 20-29, 30-39, 40-49, ….,90-99 (As our data is from 23 to 98). The grouping of data is called the “class interval” or “classes”, and the size of the class is called “class-size” or “class-width”.

In this case, the class size is 10. In each class, we have a lower-class limit and an upper-class limit. For example, if the class interval is 30-39, the lower-class limit is 30, and the upper-class limit is 39. Therefore, the least number in the class interval is called the lower-class limit and the greatest limit in the class interval is called upper-class limit.

Hence, the presentation of data in the grouped frequency table is given below:

Hence, the presentation of data in this form simplifies the data and it helps to enable the observer to understand the main feature of data at a glance.

Practice Problems

• The heights of 50 students (in cms) are given below. Present the data using the grouped frequency table by taking the class intervals as 160 -165, 165 -170, and so on.  Data: 161, 150, 154, 165, 168, 161, 154, 162, 150, 151, 162, 164, 171, 165, 158, 154, 156, 172, 160, 170, 153, 159, 161, 170, 162, 165, 166, 168, 165, 164, 154, 152, 153, 156, 158, 162, 160, 161, 173, 166, 161, 159, 162, 167, 168, 159, 158, 153, 154, 159.
• Three coins are tossed simultaneously and each time the number of heads occurring is noted and it is given below. Present the data using the frequency distribution table. Data: 0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 3, 0, 0, 1, 1, 2, 3, 2, 2, 0.

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Eclipse 2024: Time, best places to watch, latest weather forecast, ZIP code tool, what will you see?

T he Great North American eclipse is Monday, April 8 and skywatchers – with proper glasses, of course – are ready to see the moon blocking out the sun during a solar eclipse.

What you will see, how long it will last and when it will take place will depend on where you live. While all states in the contiguous U.S. will experience some level of the eclipse, Texas, Oklahoma, Arkansas, Missouri, Illinois, Indiana, Ohio, New York, Pennsylvania, Vermont, New Hampshire and Maine, as well as small parts of Kentucky, Michigan and Tennessee are along the path of totality and will experience the greatest periods of darkness.

In the U.S., the path of totality will start in Texas at 1:27 p.m. CT and will end in Maine at 3:35 p.m. ET (2:25 CT.) In those states, the periods of greatest darkness will reach up to 4 minutes, 27 seconds.

Here’s everything you need to know about the total solar eclipse 2024:

2024 eclipse primer

Total solar eclipse on April 8: Why this eclipse will be much different than the 2017 version

Scientists say the sun is approaching its maximum activity of its cycle this year, meaning it will be sending off more solar flares and eruptions from its surface — potentially making this year’s total solar eclipse much more dynamic.

Best places to watch the eclipse

Total Solar Eclipse April 8: Map shows 15 best states to see April’s total solar eclipse

The path of totality will start in Mexico and move across Texas, Oklahoma, Arkansas, Missouri, Illinois, Indiana, Ohio, New York, Pennsylvania, Vermont, New Hampshire and Maine before heading out over the North Atlantic. Small portions of Kentucky, Michigan and Tennessee will also experience almost the entirety of the eclipse. The eclipse will enter Canada in Southern Ontario, and continue through Quebec, New Brunswick, Prince Edward Island, and Nova Scotia. The eclipse will exit continental North America on the Atlantic coast of Newfoundland, Canada, at 5:16 p.m. NDT.

Where to see solar eclipse 2024: NASA eclipse map shows best places along path of totality

During the eclipse, the sky will darken as if it were dawn or dusk. Weather permitting, people in the path of totality will be able to see the sun’s corona, or outer atmosphere, which is usually obscured by the bright face of the sun, NASA explains. Outside the path of totality, viewers will see a partial eclipse with the moon covering varying degrees of the sun.

How much will you see where you live?

April 8 eclipse in Alabama: How much coverage you’ll see in your city and when

Although Alabama is not in the path of “totality” during the April 8 eclipse – meaning we won’t see total darkness when the moon covers the sun – residents will see from 78 to 92 percent coverage, depending on location.

Total solar eclipse path 2024: Search your city, ZIP code for best viewing times

People viewing the eclipse from the path of totality will be treated to the ghostly-white outer atmosphere of the sun, known as the corona, when the moon completely blocks out the sun’s disk during the total eclipse, NASA explained. Along the path, the sun will be blocked out for about 4-and-a-half minutes.

April 8 solar eclipse path of totality: What time does the eclipse start?

Wondering how much of the eclipse you will see? NASA has a tool that lets you search by city or ZIP code to see complete eclipse details. You can use this tool to see when the eclipse will start and end in every state.

Eclipse weather

Alabama solar eclipse weather: Will skies be cloudy or clear?

A big question, for a lot of the nation, is how clear the skies will be for prime eclipse viewing. An updated forecast from the National Weather Service looks like a mixed bag.

Eclipse education

Solar eclipse 2024 for kids: How to enjoy the event safely at home and in class

From building your own safety glasses to taking scientific data, researchers say there are plenty of ways to make the upcoming solar eclipse a fun learning experience for children.

Why are some schools closing for the solar eclipse?

The April 8 total solar eclipse will have millions of people gazing toward the sky as the moon tracks its way in front of the sun. And while some schools have special events planned, others – especially along the 15-state path of totality – are closing their doors that day.

NASA has a game to help kids learn about the solar eclipse: Play now

To help kids learn about solar eclipses, NASA is launching Snap It! An Eclipse Photo Adventure.

Eclipse safety

Solar eclipse 2024: Where to get free glasses to watch April 8 total solar eclipse

Skygazers planning to look at the eclipse through a camera lens or binoculars still need adequate eye protection. Without proper precaution, the sun’s rays can burn your retinas and cause severe eye injury.

Solar eclipse is Monday: 7 things to do if you’re driving that day

Crowds eager to see the eclipse are expected to be huge. According to AAA, Dallas, Austin and San Antonio are the most popular cities for eclipse viewers, followed by Indianapolis, Cleveland and Buffalo. In Dallas alone, Hertz rental car company said it is seeing six times more reservations than last year at this same time.

Solar eclipse on April 8 prompts cell phone warning

In addition to warnings about transportation systems, impacts on emergency service responses and fuel issues brought about increased demand, law enforcement said people should expect the cellular network to be strained.

How to spot fake solar eclipse glasses

Despite the ease of getting glasses, skygazers should be on the lookout for fake eclipse glasses. Real eclipse glasses are often designed with polyester film coated and coated in aluminum. Certified eclipse eyewear is designed to block all visible, and infrared light. Solar eclipse glasses must be from a vendor approved by the American Astronomical Society.

FAA issues warning ahead of April 8 total solar eclipse

The Federal Aviation Administration has issued a warning about possible travel disruptions related to the April 8 total solar eclipse.

Cell phone warning for April 8 solar eclipse: Will you be able to use your phone?

Warnings about traffic, flight congestion and emergency services are circulating ahead of the April 8 Great American Eclipse. Of particular note are concerns over cell phones and whether they will work during the eclipse.

April 8 total solar eclipse: Texas officials warn people to stock up on food ahead of solar eclipse

Mike Jones, Hays County, Texas’s direct of the Office of Emergency Services, said the area is expecting thousands of visitors to arrive to see the eclipse. To prepare for the crowds, Jones advised residents to stock up on groceries and fill up on gas. If they are out on the day of the eclipse, he recommends residents “pack your patience.”

National Guard will be deployed for total solar eclipse on April 8

At the request of local emergency management officials, the Oklahoma National Guard will have members of the 63rd Civil Support Team available to assist local governments during the eclipse, including working with first responders with additional HAZMAT responses if needed.

Total solar eclipse on April 8: How to safely look at an eclipse

Except during the brief total phase of the eclipse when the moon completely blocks the sun’s bright face, it’s not safe to look at the eclipse without specialized eye protection for solar viewing, NASA said on its eclipse information page. If you’re watching the eclipse directly, you will need solar viewing glasses – also known as eclipse glasses – or a handheld solar viewer.

Eclipse fun

Krispy Kreme is releasing a new doughnut in celebration of the solar eclipse

The doughnut chain has announced its limited-time “Total Solar Eclipse Doughnut” – an original Krispy Kreme glazed doughnut dipped in black chocolate icing and topped with silver sprinkles, piped with a buttercream made with Oreo pieces and a whole Oreo cookie in the center.

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Experts have another recommendation if you’re planning on watching the eclipse in a group or public place: Skip the neutrals and wear red and green.

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The chip brand is releasing Pineapple Habanero and Black Bean Spicy Gouda, a blend of ingredients with a nod to " sunny skies and bright days ahead while nodding to the moon with a cheesy touch.”

Sonic has new black drink for April 8 total solar eclipse and you get free eclipse glasses, too

The drive-through chain is launching a limited-edition drink called “Blackout Slush Float” to give fans an “out-of-this world experience.”

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