define tabular data presentation

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

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

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Methods of Data Collection
• 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 Questionnaires
• 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
• Quartile Deviation in Discrete Series | Formula, Calculation and Examples
• Quartile Deviation in Continuous Series | Formula, Calculation and Examples
• Mean Deviation: Coefficient of Mean Deviation, Merits, and Demerits
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Mean Deviation from Median | 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 in Statistics
• Karl Pearson's Coefficient of Correlation | Assumptions, Merits and Demerits
• 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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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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Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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7   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 .

7.1   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

7.2   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 [ From Tables to Lists ], 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?

7.2.1   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.

7.2.2   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.

7.2.3   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.

7.2.4   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

7.2.5   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 ?

7.2.6   Selecting

select name, total-grade from gradebook end

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

7.2.7   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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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.

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

How to use make.names function in r (with examples), related posts, how to normalize data between -1 and 1, vba: how to check if string contains another..., how to interpret f-values in a two-way anova, how to create a vector of ones in..., how to determine if a probability distribution is..., what is a symmetric histogram (definition & examples), how to find the mode of a histogram..., how to find quartiles in even and odd..., how to calculate sxy in statistics (with example), how to calculate sxx in statistics (with example).

• Textual And Tabular Presentation Of Data

Think about a scenario where your report cards are printed in a textual format. Your grades and remarks about you are presented in a paragraph format instead of data tables. Would be very confusing right? This is why data must be presented correctly and clearly. Let us take a look.

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Presentation of data.

Presentation of data is of utter importance nowadays. Afterall everything that’s pleasing to our eyes never fails to grab our attention. Presentation of data refers to an exhibition or putting up data in an attractive and useful manner such that it can be easily interpreted. The three main forms of presentation of data are:

• Textual presentation
• Data tables
• Diagrammatic presentation

Here we will be studying only the textual and tabular presentation, i.e. data tables in some detail.

Textual Presentation

The discussion about the presentation of data starts off with it’s most raw and vague form which is the textual presentation. In such form of presentation, data is simply mentioned as mere text, that is generally in a paragraph. This is commonly used when the data is not very large.

This kind of representation is useful when we are looking to supplement qualitative statements with some data. For this purpose, the data should not be voluminously represented in tables or diagrams. It just has to be a statement that serves as a fitting evidence to our qualitative evidence and helps the reader to get an idea of the scale of a phenomenon .

For example, “the 2002 earthquake proved to be a mass murderer of humans . As many as 10,000 citizens have been reported dead”. The textual representation of data simply requires some intensive reading. This is because the quantitative statement just serves as an evidence of the qualitative statements and one has to go through the entire text before concluding anything.

Further, if the data under consideration is large then the text matter increases substantially. As a result, the reading process becomes more intensive, time-consuming and cumbersome.

Data Tables or Tabular Presentation

A table facilitates representation of even large amounts of data in an attractive, easy to read and organized manner. The data is organized in rows and columns. This is one of the most widely used forms of presentation of data since data tables are easy to construct and read.

Components of  Data Tables

• Table Number : Each table should have a specific table number for ease of access and locating. This number can be readily mentioned anywhere which serves as a reference and leads us directly to the data mentioned in that particular table.
• Title:  A table must contain a title that clearly tells the readers about the data it contains, time period of study, place of study and the nature of classification of data .
• Headnotes:  A headnote further aids in the purpose of a title and displays more information about the table. Generally, headnotes present the units of data in brackets at the end of a table title.
• Stubs:  These are titles of the rows in a table. Thus a stub display information about the data contained in a particular row.
• Caption:  A caption is the title of a column in the data table. In fact, it is a counterpart if a stub and indicates the information contained in a column.
• Body or field:  The body of a table is the content of a table in its entirety. Each item in a body is known as a ‘cell’.
• Footnotes:  Footnotes are rarely used. In effect, they supplement the title of a table if required.
• Source:  When using data obtained from a secondary source, this source has to be mentioned below the footnote.

Construction of Data Tables

There are many ways for construction of a good table. However, some basic ideas are:

• The title should be in accordance with the objective of study:  The title of a table should provide a quick insight into the table.
• Comparison:  If there might arise a need to compare any two rows or columns then these might be kept close to each other.
• Alternative location of stubs:  If the rows in a data table are lengthy, then the stubs can be placed on the right-hand side of the table.
• Headings:  Headings should be written in a singular form. For example, ‘good’ must be used instead of ‘goods’.
• Footnote:  A footnote should be given only if needed.
• Size of columns:  Size of columns must be uniform and symmetrical.
• Use of abbreviations:  Headings and sub-headings should be free of abbreviations.
• Units: There should be a clear specification of units above the columns.

The Advantages of Tabular Presentation

• Ease of representation:  A large amount of data can be easily confined in a data table. Evidently, it is the simplest form of data presentation.
• Ease of analysis:  Data tables are frequently used for statistical analysis like calculation of central tendency, dispersion etc.
• Helps in comparison:  In a data table, the rows and columns which are required to be compared can be placed next to each other. To point out, this facilitates comparison as it becomes easy to compare each value.
• Economical:  Construction of a data table is fairly easy and presents the data in a manner which is really easy on the eyes of a reader. Moreover, it saves time as well as space.

Classification of Data and Tabular Presentation

Qualitative classification.

In this classification, data in a table is classified on the basis of qualitative attributes. In other words, if the data contained attributes that cannot be quantified like rural-urban, boys-girls etc. it can be identified as a qualitative classification of data.

Quantitative Classification

In quantitative classification, data is classified on basis of quantitative attributes.

Temporal Classification

Here data is classified according to time. Thus when data is mentioned with respect to different time frames, we term such a classification as temporal.

Spatial Classification

When data is classified according to a location, it becomes a spatial classification.

A Solved Example for You

Q:  The classification in which data in a table is classified according to time is known as:

• Qualitative
• Quantitative

Ans:  The form of classification in which data is classified based on time frames is known as the temporal classification of data and tabular presentation.

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• Diagrammatic Presentation of Data

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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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10 Methods of Data Presentation with 5 Great Tips to Practice, Best in 2024

Leah Nguyen • 05 April, 2024 • 17 min read

There are different ways of presenting data, so which one is suited you the most? You can end deathly boring and ineffective data presentation right now with our 10 methods of data presentation . Check out the examples from each technique!

Have you ever presented a data report to your boss/coworkers/teachers thinking it was super dope like you’re some cyber hacker living in the Matrix, but all they saw was a pile of static numbers that seemed pointless and didn’t make sense to them?

Understanding digits is rigid . Making people from non-analytical backgrounds understand those digits is even more challenging.

How can you clear up those confusing numbers in the types of presentation that have the flawless clarity of a diamond? So, let’s check out best way to present data. 💎

Table of Contents

• What are Methods of Data Presentations?
• #1 – Tabular

#3 – Pie chart

#4 – bar chart, #5 – histogram, #6 – line graph, #7 – pictogram graph, #8 – radar chart, #9 – heat map, #10 – scatter plot.

• 5 Mistakes to Avoid
• Best Method of Data Presentation

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What are Methods of Data Presentation?

The term ’data presentation’ relates to the way you present data in a way that makes even the most clueless person in the room understand. 

Some say it’s witchcraft (you’re manipulating the numbers in some ways), but we’ll just say it’s the power of turning dry, hard numbers or digits into a visual showcase that is easy for people to digest.

Presenting data correctly can help your audience understand complicated processes, identify trends, and instantly pinpoint whatever is going on without exhausting their brains.

Good data presentation helps…

• Make informed decisions and arrive at positive outcomes . If you see the sales of your product steadily increase throughout the years, it’s best to keep milking it or start turning it into a bunch of spin-offs (shoutout to Star Wars👀).
• Reduce the time spent processing data . Humans can digest information graphically 60,000 times faster than in the form of text. Grant them the power of skimming through a decade of data in minutes with some extra spicy graphs and charts.
• Communicate the results clearly . Data does not lie. They’re based on factual evidence and therefore if anyone keeps whining that you might be wrong, slap them with some hard data to keep their mouths shut.
• Add to or expand the current research . You can see what areas need improvement, as well as what details often go unnoticed while surfing through those little lines, dots or icons that appear on the data board.

Methods of Data Presentation and Examples

Imagine you have a delicious pepperoni, extra-cheese pizza. You can decide to cut it into the classic 8 triangle slices, the party style 12 square slices, or get creative and abstract on those slices. 

There are various ways for cutting a pizza and you get the same variety with how you present your data. In this section, we will bring you the 10 ways to slice a pizza – we mean to present your data – that will make your company’s most important asset as clear as day. Let’s dive into 10 ways to present data efficiently.

#1 – Tabular 

Among various types of data presentation, tabular is the most fundamental method, with data presented in rows and columns. Excel or Google Sheets would qualify for the job. Nothing fancy.

This is an example of a tabular presentation of data on Google Sheets. Each row and column has an attribute (year, region, revenue, etc.), and you can do a custom format to see the change in revenue throughout the year.

When presenting data as text, all you do is write your findings down in paragraphs and bullet points, and that’s it. A piece of cake to you, a tough nut to crack for whoever has to go through all of the reading to get to the point.

• 65% of email users worldwide access their email via a mobile device.
• Emails that are optimised for mobile generate 15% higher click-through rates.
• 56% of brands using emojis in their email subject lines had a higher open rate.

(Source: CustomerThermometer )

All the above quotes present statistical information in textual form. Since not many people like going through a wall of texts, you’ll have to figure out another route when deciding to use this method, such as breaking the data down into short, clear statements, or even as catchy puns if you’ve got the time to think of them.

A pie chart (or a ‘donut chart’ if you stick a hole in the middle of it) is a circle divided into slices that show the relative sizes of data within a whole. If you’re using it to show percentages, make sure all the slices add up to 100%.

The pie chart is a familiar face at every party and is usually recognised by most people. However, one setback of using this method is our eyes sometimes can’t identify the differences in slices of a circle, and it’s nearly impossible to compare similar slices from two different pie charts, making them the villains in the eyes of data analysts.

Bonus example: A literal ‘pie’ chart! 🥧

The bar chart is a chart that presents a bunch of items from the same category, usually in the form of rectangular bars that are placed at an equal distance from each other. Their heights or lengths depict the values they represent.

They can be as simple as this:

Or more complex and detailed like this example of presentation of data. Contributing to an effective statistic presentation, this one is a grouped bar chart that not only allows you to compare categories but also the groups within them as well.

Similar in appearance to the bar chart but the rectangular bars in histograms don’t often have the gap like their counterparts.

Instead of measuring categories like weather preferences or favourite films as a bar chart does, a histogram only measures things that can be put into numbers.

Teachers can use presentation graphs like a histogram to see which score group most of the students fall into, like in this example above.

Recordings to ways of displaying data, we shouldn’t overlook the effectiveness of line graphs. Line graphs are represented by a group of data points joined together by a straight line. There can be one or more lines to compare how several related things change over time. 

On a line chart’s horizontal axis, you usually have text labels, dates or years, while the vertical axis usually represents the quantity (e.g.: budget, temperature or percentage).

A pictogram graph uses pictures or icons relating to the main topic to visualise a small dataset. The fun combination of colours and illustrations makes it a frequent use at schools.

Pictograms are a breath of fresh air if you want to stay away from the monotonous line chart or bar chart for a while. However, they can present a very limited amount of data and sometimes they are only there for displays and do not represent real statistics.

If presenting five or more variables in the form of a bar chart is too stuffy then you should try using a radar chart, which is one of the most creative ways to present data.

Radar charts show data in terms of how they compare to each other starting from the same point. Some also call them ‘spider charts’ because each aspect combined looks like a spider web.

Radar charts can be a great use for parents who’d like to compare their child’s grades with their peers to lower their self-esteem. You can see that each angular represents a subject with a score value ranging from 0 to 100. Each student’s score across 5 subjects is highlighted in a different colour.

If you think that this method of data presentation somehow feels familiar, then you’ve probably encountered one while playing Pokémon .

A heat map represents data density in colours. The bigger the number, the more colour intense that data will be represented.

Most U.S citizens would be familiar with this data presentation method in geography. For elections, many news outlets assign a specific colour code to a state, with blue representing one candidate and red representing the other. The shade of either blue or red in each state shows the strength of the overall vote in that state.

Another great thing you can use a heat map for is to map what visitors to your site click on. The more a particular section is clicked the ‘hotter’ the colour will turn, from blue to bright yellow to red.

If you present your data in dots instead of chunky bars, you’ll have a scatter plot. 

A scatter plot is a grid with several inputs showing the relationship between two variables. It’s good at collecting seemingly random data and revealing some telling trends.

For example, in this graph, each dot shows the average daily temperature versus the number of beach visitors across several days. You can see that the dots get higher as the temperature increases, so it’s likely that hotter weather leads to more visitors.

5 Data Presentation Mistakes to Avoid

#1 – assume your audience understands what the numbers represent.

You may know all the behind-the-scenes of your data since you’ve worked with them for weeks, but your audience doesn’t.

Showing without telling only invites more and more questions from your audience, as they have to constantly make sense of your data, wasting the time of both sides as a result.

While showing your data presentations, you should tell them what the data are about before hitting them with waves of numbers first. You can use interactive activities such as polls , word clouds , online quiz and Q&A sections , combined with icebreaker games , to assess their understanding of the data and address any confusion beforehand.

#2 – Use the wrong type of chart

Charts such as pie charts must have a total of 100% so if your numbers accumulate to 193% like this example below, you’re definitely doing it wrong.

Before making a chart, ask yourself: what do I want to accomplish with my data? Do you want to see the relationship between the data sets, show the up and down trends of your data, or see how segments of one thing make up a whole?

Remember, clarity always comes first. Some data visualisations may look cool, but if they don’t fit your data, steer clear of them. 

#3 – Make it 3D

3D is a fascinating graphical presentation example. The third dimension is cool, but full of risks.

Can you see what’s behind those red bars? Because we can’t either. You may think that 3D charts add more depth to the design, but they can create false perceptions as our eyes see 3D objects closer and bigger than they appear, not to mention they cannot be seen from multiple angles.

#4 – Use different types of charts to compare contents in the same category

This is like comparing a fish to a monkey. Your audience won’t be able to identify the differences and make an appropriate correlation between the two data sets. 

Next time, stick to one type of data presentation only. Avoid the temptation of trying various data visualisation methods in one go and make your data as accessible as possible.

#5 – Bombard the audience with too much information

The goal of data presentation is to make complex topics much easier to understand, and if you’re bringing too much information to the table, you’re missing the point.

The more information you give, the more time it will take for your audience to process it all. If you want to make your data understandable and give your audience a chance to remember it, keep the information within it to an absolute minimum. You should set your session with open-ended questions , to avoid dead-communication!

What are the Best Methods of Data Presentation?

Finally, which is the best way to present data?

The answer is…

There is none 😄 Each type of presentation has its own strengths and weaknesses and the one you choose greatly depends on what you’re trying to do. 

For example:

• Go for a scatter plot if you’re exploring the relationship between different data values, like seeing whether the sales of ice cream go up because of the temperature or because people are just getting more hungry and greedy each day?
• Go for a line graph if you want to mark a trend over time. 
• Go for a heat map if you like some fancy visualisation of the changes in a geographical location, or to see your visitors’ behaviour on your website.
• Go for a pie chart (especially in 3D) if you want to be shunned by others because it was never a good idea👇

What is chart presentation?

A chart presentation is a way of presenting data or information using visual aids such as charts, graphs, and diagrams. The purpose of a chart presentation is to make complex information more accessible and understandable for the audience.

When can I use charts for presentation?

Charts can be used to compare data, show trends over time, highlight patterns, and simplify complex information.

Why should use charts for presentation?

You should use charts to ensure your contents and visual look clean, as they are the visual representative, provide clarity, simplicity, comparison, contrast and super time-saving!

What are the 4 graphical methods of presenting data?

Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Leah Nguyen

Words that convert, stories that stick. I turn complex ideas into engaging narratives - helping audiences learn, remember, and take action.

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Presentation of Data in Tables (Tabulation of Data)

Reference: • Health information and basic medical statistics: Park’s Textbook of PSM, 23rd ed. 2016 • Methods in Biostatistics: B.K. Mahajan, Jaypee Brothers Medical Publishers • Informative Presentation of Tables, Graphs and Statistics: University of Reading, Statistical Services Centre. Biometrics Advisory and Support Service to DFID, March 2000 • Making Data Meaningful, A guide to presenting statistics, UNITED NATIONS, Geneva, 2009

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Blog Data Visualization 10 Data Presentation Examples For Strategic Communication

10 Data Presentation Examples For Strategic Communication

Written by: Krystle Wong Sep 28, 2023

Knowing how to present data is like having a superpower. 

Data presentation today is no longer just about numbers on a screen; it’s storytelling with a purpose. It’s about captivating your audience, making complex stuff look simple and inspiring action. 

To help turn your data into stories that stick, influence decisions and make an impact, check out Venngage’s free chart maker or follow me on a tour into the world of data storytelling along with data presentation templates that work across different fields, from business boardrooms to the classroom and beyond. Keep scrolling to learn more! 

Click to jump ahead:

10 Essential data presentation examples + methods you should know

What should be included in a data presentation, what are some common mistakes to avoid when presenting data, faqs on data presentation examples, transform your message with impactful data storytelling.

Data presentation is a vital skill in today’s information-driven world. Whether you’re in business, academia, or simply want to convey information effectively, knowing the different ways of presenting data is crucial. For impactful data storytelling, consider these essential data presentation methods:

1. Bar graph

Ideal for comparing data across categories or showing trends over time.

Bar graphs, also known as bar charts are workhorses of data presentation. They’re like the Swiss Army knives of visualization methods because they can be used to compare data in different categories or display data changes over time. 

In a bar chart, categories are displayed on the x-axis and the corresponding values are represented by the height of the bars on the y-axis. 

It’s a straightforward and effective way to showcase raw data, making it a staple in business reports, academic presentations and beyond.

Make sure your bar charts are concise with easy-to-read labels. Whether your bars go up or sideways, keep it simple by not overloading with too many categories.

2. Line graph

Great for displaying trends and variations in data points over time or continuous variables.

Line charts or line graphs are your go-to when you want to visualize trends and variations in data sets over time.

One of the best quantitative data presentation examples, they work exceptionally well for showing continuous data, such as sales projections over the last couple of years or supply and demand fluctuations. 

The x-axis represents time or a continuous variable and the y-axis represents the data values. By connecting the data points with lines, you can easily spot trends and fluctuations.

A tip when presenting data with line charts is to minimize the lines and not make it too crowded. Highlight the big changes, put on some labels and give it a catchy title.

3. Pie chart

Useful for illustrating parts of a whole, such as percentages or proportions.

Pie charts are perfect for showing how a whole is divided into parts. They’re commonly used to represent percentages or proportions and are great for presenting survey results that involve demographic data. 

Each “slice” of the pie represents a portion of the whole and the size of each slice corresponds to its share of the total. 

While pie charts are handy for illustrating simple distributions, they can become confusing when dealing with too many categories or when the differences in proportions are subtle.

Don’t get too carried away with slices — label those slices with percentages or values so people know what’s what and consider using a legend for more categories.

4. Scatter plot

Effective for showing the relationship between two variables and identifying correlations.

Scatter plots are all about exploring relationships between two variables. They’re great for uncovering correlations, trends or patterns in data. 

In a scatter plot, every data point appears as a dot on the chart, with one variable marked on the horizontal x-axis and the other on the vertical y-axis.

By examining the scatter of points, you can discern the nature of the relationship between the variables, whether it’s positive, negative or no correlation at all.

If you’re using scatter plots to reveal relationships between two variables, be sure to add trendlines or regression analysis when appropriate to clarify patterns. Label data points selectively or provide tooltips for detailed information.

5. Histogram

Best for visualizing the distribution and frequency of a single variable.

Histograms are your choice when you want to understand the distribution and frequency of a single variable. 

They divide the data into “bins” or intervals and the height of each bar represents the frequency or count of data points falling into that interval. 

Histograms are excellent for helping to identify trends in data distributions, such as peaks, gaps or skewness.

Here’s something to take note of — ensure that your histogram bins are appropriately sized to capture meaningful data patterns. Using clear axis labels and titles can also help explain the distribution of the data effectively.

6. Stacked bar chart

Useful for showing how different components contribute to a whole over multiple categories.

Stacked bar charts are a handy choice when you want to illustrate how different components contribute to a whole across multiple categories. 

Each bar represents a category and the bars are divided into segments to show the contribution of various components within each category. 

This method is ideal for highlighting both the individual and collective significance of each component, making it a valuable tool for comparative analysis.

Stacked bar charts are like data sandwiches—label each layer so people know what’s what. Keep the order logical and don’t forget the paintbrush for snazzy colors. Here’s a data analysis presentation example on writers’ productivity using stacked bar charts:

7. Area chart

Similar to line charts but with the area below the lines filled, making them suitable for showing cumulative data.

Area charts are close cousins of line charts but come with a twist. 

Imagine plotting the sales of a product over several months. In an area chart, the space between the line and the x-axis is filled, providing a visual representation of the cumulative total. 

This makes it easy to see how values stack up over time, making area charts a valuable tool for tracking trends in data.

For area charts, use them to visualize cumulative data and trends, but avoid overcrowding the chart. Add labels, especially at significant points and make sure the area under the lines is filled with a visually appealing color gradient.

8. Tabular presentation

Presenting data in rows and columns, often used for precise data values and comparisons.

Tabular data presentation is all about clarity and precision. Think of it as presenting numerical data in a structured grid, with rows and columns clearly displaying individual data points. 

A table is invaluable for showcasing detailed data, facilitating comparisons and presenting numerical information that needs to be exact. They’re commonly used in reports, spreadsheets and academic papers.

When presenting tabular data, organize it neatly with clear headers and appropriate column widths. Highlight important data points or patterns using shading or font formatting for better readability.

9. Textual data

Utilizing written or descriptive content to explain or complement data, such as annotations or explanatory text.

Textual data presentation may not involve charts or graphs, but it’s one of the most used qualitative data presentation examples. 

It involves using written content to provide context, explanations or annotations alongside data visuals. Think of it as the narrative that guides your audience through the data. 

Well-crafted textual data can make complex information more accessible and help your audience understand the significance of the numbers and visuals.

Textual data is your chance to tell a story. Break down complex information into bullet points or short paragraphs and use headings to guide the reader’s attention.

10. Pictogram

Using simple icons or images to represent data is especially useful for conveying information in a visually intuitive manner.

Pictograms are all about harnessing the power of images to convey data in an easy-to-understand way. 

Instead of using numbers or complex graphs, you use simple icons or images to represent data points. 

For instance, you could use a thumbs up emoji to illustrate customer satisfaction levels, where each face represents a different level of satisfaction. 

Pictograms are great for conveying data visually, so choose symbols that are easy to interpret and relevant to the data. Use consistent scaling and a legend to explain the symbols’ meanings, ensuring clarity in your presentation.

Looking for more data presentation ideas? Use the Venngage graph maker or browse through our gallery of chart templates to pick a template and get started! 

A comprehensive data presentation should include several key elements to effectively convey information and insights to your audience. Here’s a list of what should be included in a data presentation:

1. Title and objective

• Begin with a clear and informative title that sets the context for your presentation.
• State the primary objective or purpose of the presentation to provide a clear focus.

2. Key data points

• Present the most essential data points or findings that align with your objective.
• Use charts, graphical presentations or visuals to illustrate these key points for better comprehension.

3. Context and significance

• Provide a brief overview of the context in which the data was collected and why it’s significant.
• Explain how the data relates to the larger picture or the problem you’re addressing.

4. Key takeaways

• Summarize the main insights or conclusions that can be drawn from the data.
• Highlight the key takeaways that the audience should remember.

5. Visuals and charts

• Use clear and appropriate visual aids to complement the data.
• Ensure that visuals are easy to understand and support your narrative.

6. Implications or actions

• Discuss the practical implications of the data or any recommended actions.
• If applicable, outline next steps or decisions that should be taken based on the data.

7. Q&A and discussion

• Allocate time for questions and open discussion to engage the audience.
• Address queries and provide additional insights or context as needed.

Presenting data is a crucial skill in various professional fields, from business to academia and beyond. To ensure your data presentations hit the mark, here are some common mistakes that you should steer clear of:

Overloading with data

Presenting too much data at once can overwhelm your audience. Focus on the key points and relevant information to keep the presentation concise and focused. Here are some free data visualization tools you can use to convey data in an engaging and impactful way. 

Assuming everyone’s on the same page

It’s easy to assume that your audience understands as much about the topic as you do. But this can lead to either dumbing things down too much or diving into a bunch of jargon that leaves folks scratching their heads. Take a beat to figure out where your audience is coming from and tailor your presentation accordingly.

Misleading visuals

Using misleading visuals, such as distorted scales or inappropriate chart types can distort the data’s meaning. Pick the right data infographics and understandable charts to ensure that your visual representations accurately reflect the data.

Not providing context

Data without context is like a puzzle piece with no picture on it. Without proper context, data may be meaningless or misinterpreted. Explain the background, methodology and significance of the data.

Not citing sources properly

Neglecting to cite sources and provide citations for your data can erode its credibility. Always attribute data to its source and utilize reliable sources for your presentation.

Not telling a story

Avoid simply presenting numbers. If your presentation lacks a clear, engaging story that takes your audience on a journey from the beginning (setting the scene) through the middle (data analysis) to the end (the big insights and recommendations), you’re likely to lose their interest.

Infographics are great for storytelling because they mix cool visuals with short and sweet text to explain complicated stuff in a fun and easy way. Create one with Venngage’s free infographic maker to create a memorable story that your audience will remember.

Ignoring data quality

Presenting data without first checking its quality and accuracy can lead to misinformation. Validate and clean your data before presenting it.

Simplify your visuals

Fancy charts might look cool, but if they confuse people, what’s the point? Go for the simplest visual that gets your message across. Having a dilemma between presenting data with infographics v.s data design? This article on the difference between data design and infographics might help you out. 

Missing the emotional connection

Data isn’t just about numbers; it’s about people and real-life situations. Don’t forget to sprinkle in some human touch, whether it’s through relatable stories, examples or showing how the data impacts real lives.

Skipping the actionable insights

At the end of the day, your audience wants to know what they should do with all the data. If you don’t wrap up with clear, actionable insights or recommendations, you’re leaving them hanging. Always finish up with practical takeaways and the next steps.

Can you provide some data presentation examples for business reports?

Business reports often benefit from data presentation through bar charts showing sales trends over time, pie charts displaying market share,or tables presenting financial performance metrics like revenue and profit margins.

What are some creative data presentation examples for academic presentations?

Creative data presentation ideas for academic presentations include using statistical infographics to illustrate research findings and statistical data, incorporating storytelling techniques to engage the audience or utilizing heat maps to visualize data patterns.

What are the key considerations when choosing the right data presentation format?

When choosing a chart format , consider factors like data complexity, audience expertise and the message you want to convey. Options include charts (e.g., bar, line, pie), tables, heat maps, data visualization infographics and interactive dashboards.

Knowing the type of data visualization that best serves your data is just half the battle. Here are some best practices for data visualization to make sure that the final output is optimized. 

How can I choose the right data presentation method for my data?

To select the right data presentation method, start by defining your presentation’s purpose and audience. Then, match your data type (e.g., quantitative, qualitative) with suitable visualization techniques (e.g., histograms, word clouds) and choose an appropriate presentation format (e.g., slide deck, report, live demo).

For more presentation ideas , check out this guide on how to make a good presentation or use a presentation software to simplify the process.  

How can I make my data presentations more engaging and informative?

To enhance data presentations, use compelling narratives, relatable examples and fun data infographics that simplify complex data. Encourage audience interaction, offer actionable insights and incorporate storytelling elements to engage and inform effectively.

The opening of your presentation holds immense power in setting the stage for your audience. To design a presentation and convey your data in an engaging and informative, try out Venngage’s free presentation maker to pick the right presentation design for your audience and topic. 

What is the difference between data visualization and data presentation?

Data presentation typically involves conveying data reports and insights to an audience, often using visuals like charts and graphs. Data visualization , on the other hand, focuses on creating those visual representations of data to facilitate understanding and analysis. 

Now that you’ve learned a thing or two about how to use these methods of data presentation to tell a compelling data story , it’s time to take these strategies and make them your own. 

But here’s the deal: these aren’t just one-size-fits-all solutions. Remember that each example we’ve uncovered here is not a rigid template but a source of inspiration. It’s all about making your audience go, “Wow, I get it now!”

Think of your data presentations as your canvas – it’s where you paint your story, convey meaningful insights and make real change happen. 

So, go forth, present your data with confidence and purpose and watch as your strategic influence grows, one compelling presentation at a time.

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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.

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

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

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

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

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.

TABULAR PRESENTATION OF DATA

Tabulation may be defined as systematic presentation of data with the help of a statistical table having a number of rows and columns and complete with reference number, title, description of rows as well as columns and foot notes, if any.

We may consider the following guidelines for tabulation :

1.  A statistical table should be allotted a serial number along with a self-explanatory title.

2. The table under consideration should be divided into caption, Box-head, Stub and Body.

Caption is the upper part of the table, describing the columns and sub-columns, if any.

The Box-head is the entire upper part of the table which includes columns and sub-column numbers, unit(s) of measurement along with caption.

Stub is the left part of the table providing the description of the rows.

The body is the main part of the table that contains the numerical figures.

3. The table should be well-balanced in length and breadth.

4.  The data must be arranged in a table in such a way that comparison(s) between different figures are made possible without much labor and time.

Also the row totals, column totals, the units of measurement must be shown.

5. The data should be arranged intelligently in a well-balanced sequence and the presentation of data in the table should be appealing to the eyes as far as practicable.

6.  Notes describing the source of the data and bringing clarity and, if necessary, about any rows or columns known as footnotes, should be shown at the bottom part of the table.

The textual presentation of data, relating to the workers of a factory is shown in the following table.

Status of the workers of the factory on the basis of their trade union membership for 1999 and 2000.

Here, we have to write the source through which we got the above data.

TU, M, F and T stand for trade union, male, female and total respectively.

The tabulation method is usually preferred to textual presentation as

(i)  It facilitates comparison between rows and columns.

(ii) Complicated data can also be represented using tabulation.

(iii)  It is a must for diagrammatic representation.

(iv)  Without tabulation, statistical analysis of data is not possible.

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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

(Image will be uploaded soon)

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

(image will be uploaded soon)

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.

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TEXTUAL, TABULAR & DIAGRAMMATIC PRESENTATION OF DATA

STATISTICS : PRESENTATION OF DATA

Data can be presented in three ways:

• Textual presentation
• Tabular presentation
• Diagrammatic presentation

1. Textual Mode of presentation is  layman’s method of presentation of data.  Anyone can prepare, anyone can understand. No specific skill(s) is/are required.

2. Tabular Mode of presentation is  the most accurate mode of presentation of data.  It requires a lot of skill to prepare, and some skill(s) to understand. Table facilitates comparison.

But, Table should be good enough as per some points of view:

• 1. Appealing
• 2. Well-balanced
• 3. Compulsory Title and Table Number
• 4. Title should be  self-explanatory
• 5. Units must be properly mentioned
• 6. Comparison should be easy
• 7. Sources and footnotes (if any) must be mentioned at the bottom

Below is a sample of how a table should look like:

Table No. 1: Format of a table

* Sources: 1. Kailasha Foundation – Fun & Learn Portal LMS Directory *Footnotes: The entire upper part of the table is called BOX HEAD.

3. Diagrammatic Mode of Presentation:

A. Non-Frequency Diagrams: Non-frequency diagrams correspond to the data  which are NOT frequency data.  (a) Bar Diagrams (b) Line Diagrams (Historiagram) (c) Pie Diagram or Pie Chart

B. Frequency Diagrams: Frequency Data are presented. Mostly class-intervals are presented via this mode. Three most common frequency diagrams are: (a) Histogram (b) Frequency Polygon (c) Ogives: (i) Less than type Ogives (ii) More than type Ogives

• 1. Bar Diagram and Line Diagram are inter-convertible
• 2. Bar Diagram and Line Diagram can both be of simple and multiple types
• 3. Multiple bar diagram or Multiple Line diagram is used when two related series (in same unit) are to be compared
• 4. Multiple axis bar diagram or Multiple axis Line diagram is used when units in the two series are different

ILLUSTRATIONS OF PRESENTATION OF DATA:

Bar Diagrams:

Line Diagram:

Multiple  Bar Diagram:

Frequency Polygon:

FREQUENCY CURVE:

A smooth join of all vertices of a frequency polygon. This is broadly divided into four shapes:

(i) Bell Shaped (Most Common Shape) (ii) U-Shaped (iii) J – Shaped: Simple J – shaped & Inverted J – Shaped (iv) Mixed Curve (Second Most Common Shape)

• 1. CENSUS: The collection of data from every element in a population or universe or arena of statistical enquiry.
• 2. SAMPLE: The collection of data from subgroup or subset of the population.
• 3. FREQUENCY: The number of times a certain value or class of values occurs.
• 4. CUMULATIVE FREQUENCY: The running total of the frequencies at each class interval level.
• 5. FREQUENCY DISTRIBUTION: The organization of raw data in table form with classes and frequencies.
• 6. CLASS LIMITS: The  originally assigned extreme values  of classes are called class limits, viz. Lower class limit and upper class limit.
• 7. CLASS WIDTH: The difference between the upper and lower boundaries  (NOT limits) of any class.
• 8. CLASS BOUNDARY: After making the distribution continuous, the upper class boundary of a class becomes equal to the lower class boundary of the next class.
• 9. CLASS MARK: The mid-point of any class is called the class mark.

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Hindi explanation:.

ENGLISH EXPLANATION:

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