a diagrammatic representation of numerical data

Graphical Representation of Data

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

Definition of Graphical Representation of Data

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

Representation of Data

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

Principles of Graphical Representation of Data

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

Advantages and Disadvantages of Graphical Representation of Data

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

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

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

Rules of Graphical Representation of Data

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

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

Uses of Graphical Representation of Data

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

Types of Graphical Representation of Data

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

Related Topics

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

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

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

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

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

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

Hence, mode = 54

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

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

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

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

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Practice Questions on Graphical Representation of Data

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

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

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

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

What is the Use of Graphical Representation of Data?

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

What are the Ways to Represent Data?

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

What is the Objective of Graphical Representation of Data?

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

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• CBSE Class 11 Statistics for Economics Notes

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

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

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

Chapter 3: Organisation of Data

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

Chapter 4: Presentation of Data: Textual and Tabular

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

Chapter 5: Diagrammatic Presentation of Data

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

Diagrammatic and Graphic Presentation of Data

Chapter 6: measures of central tendency: arithmetic mean.

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

Chapter 7: Measures of Central Tendency: Median and Mode

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

Chapter 8: Measures of Dispersion

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

Chapter 9: Correlation

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

Chapter 10: Index Number

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

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

Diagrammatic and graphic presentation of data means visual representation of the data. It shows a comparison between two or more sets of data and helps in the presentation of highly complex data in its simplest form. Diagrams and graphs are clear and easy to read and understand. In the diagrammatic presentation of data, bar charts, rectangles, sub-divided rectangles, pie charts, or circle diagrams are used. In the graphic presentation of data, graphs like histograms, frequency polygon, frequency curves, cumulative frequency polygon, and graphs of time series are used.

General Rules for Construction of Diagrammatic and Graphic Presentations: 

1. Chronic Number: Each outline or chart should have a chronic number. It is important to recognize one from the other.

2. Title: A title should be given to each outline or chart. From the title, one can understand what the graph or diagram is. The title ought to be brief and simple. It is normally positioned at the top.

3. Legitimate size and scale: An outline or chart ought to be of ordinary size and drawn with an appropriate scale. The scale in a chart indicates the size of the unit.

4. Neatness: Outlines should be pretty much as straightforward as could be expected. Further, they should be very perfect and clean. They ought to likewise be dropped to check out.

5. File: Each outline or chart should be joined by a record. This outlines various sorts of lines, shades or tones utilized in the graph.

6. Commentary: Commentaries might be given at the lower part of an outline. It explains specific focuses in the chart.

Merits of Diagrammatic and Graphics Presentation:

The fundamental benefits or merits of a diagrammatic and graphical representation of data are as follows:

1. To simplify the data: Outlines and charts present information in a simple manner that can be perceived by anyone without any problem. Huge volume of data can be easily presented using graphs and diagrams.

2. Appealing presentation: Outlines and charts present complex information and data in an understandable and engaging manner and leave a great visual effect. In this way, the diagrammatic and graphical representation of information effectively draws the attention of users.

3. Helps with comparison of data: With the help of outlines and charts, comparison and examination data between various arrangements of information is possible.

4. Helps in forecasting: The diagrammatic and graphical representation of information has past patterns, which helps in forecasting and making various policies for the future.

5. Saves time and labour: Charts and graphs make the complex data into a simple form, which can be easily understood by anyone without having prior knowledge of the data. It gives ready to use information, and the user can use it accordingly. In this way, it saves a lot of time and labour.

6. Universally acceptable: Graphs and diagrams are used in every field and can be easily understood by anyone. Hence they are universally acceptable.

7. Helps in decision making: Diagrams and graphs give the real data about the past patterns, trends, outcomes, etc., which helps in future preparation.

Demerits of Diagrammatic and Graphics Presentation:

The demerits of diagrammatic and graphics presentation of data are as follows:

1. Handle with care: Drawing, surmising and understanding from graphs and diagrams needs proper insight and care. A person with little knowledge of statistics cannot analyze or use the data properly.

2. Specific information: Graphs and diagrams do not depict true or precise information. They are generally founded on approximations. The information provided is limited and specific.

3. Low precision: Graphs and diagrams can give misleading results, as they are mostly based on approximation of data. Personal judgement is used to study or analyze the data, which can make the information biased. Also, data can easily be manipulated.

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45 Presentation of data I – Diagrammatic representation

Pa . Raajeswari

INTRODUCTION

The data we collect can often be more easily understood for interpretation if it is presented graphically or pictorially. Diagrams and graphs give visual indication of magnitudes, grouping, trends and patterns in the data. The diagrams are used for facilitating comparisons between two or more sets of data. The diagrams are more suitable to illustrate the discrete data. The diagrams should be clear and easy to read and understand.

A large number of diagrams are used to present statistical data. The choice of a particular diagram to present a given set of numerical data is not an easy one. It primarily depends on the nature of the data, magnitude of the observations and the type of people for whom the diagrams are meant and requires great amount of expertise, skill and intelligence. An inappropriate choice of the diagram for the given set of data might give a distorted picture of the phenomenon under the study and might lead to wrong and fallacious interpretations and conclusions. Hence, the choice of a diagram to present the given data should be made with utmost caution and care. The diagrams do not add any meaning to the statistical facts, but they exhibit the results more clearly. Use of diagrams is becoming more and morepopular in the present scenario.

REPRESENTATION OF DATA

Besides the tabular form, the data may also be presented in some graphic or diagrammatic form. “The transformation of data through visual methods like graphs, diagrams, maps and charts is called representation of data.”

The need of representing data graphically:

Graphics, such as maps, graphs and diagrams, are used to represent large volume of data. They are necessary:

• If the information is presented in tabular form or in a descriptive  record, it becomes difficult to draw results.
• Diagramatic form makes it possible to easily draw visual impressions of data.
• The diagramatic method of the representation of data enhances our understanding.
• It makes the comparisons easy.
• Besides, such methods create an imprint on mind for a longer time.
• Diagrams are visual aids for presentation of statistical data and more appealing.
• It is a time consuming task to draw inferences about whatever is being presented in non–diagramaticform.
• It presents characteristics in a simplified way.
• These makes it easy to understand the patterns of population growth, distribution and the density, sex ratio, age–sex composition, occupational structure, etc.

General Rules for Drawing Diagrams and Maps

1. Selection of a Suitable Diagrammatic Method

Each characteristic of the data can only be suitably represented by an appropriate diagramatic method. For example,

To show the data related to the temperature or growth of population between different periods in time line graph are used.

Similarly, bar diagrams are used for showing rainfall or the production of commodities.

The population distribution, both human and livestock, or the distribution of the crop producing areas are shown by dot maps.

The population density can be shown by choropleth maps.

Thus, it is necessary and important to select suitable diagramatic method to represent data.

2. Selection of Suitable Scale

Each diagram or map is drawn to a scale which is used to measure the data. The scale must cover the entire data that is to be represented. The scale should neither be too large nor too small.

The diagram or map should have following design:

1.  Title: The title of the diagram/map must be clear and include – o The name of the area,  Reference year of the data used and o The caption of the diagram.

These are written with different font sizes and thickness. The title, subtitle and the corresponding year is shown in the centre at the top of the map/diagram.

2.   Legend or Index : The index must clearly explain the colours, shades, symbols and signs used in the map and diagram. A legend is shown either at the lower left or lower right side of the map sheet.

3.  Direction The maps should show the direction North and properly placed on the top.

Types of Diagrams

A research should contain a large variety of diagrammatic presentations to present the data and findings of research work.

• One dimensional diagrams – Line and Bar diagram.
• Two dimensional diagrams – Pie diagram
• Three dimensional diagram – Cubes,Squares,Prisms, Cylinders and Blocks.
• Pictographs

ONE DIMENSIONAL DIAGRAMS

1.    LINE DIAGRAM

This kind of a diagram becomes suitable for representing data supplied chronologically in an ascending or descending order. It shows the behaviour of a variable over time. The line graphs are usually drawn to represent the time series data related to the temperature, rainfall, population growth, birth rates and the death rates.

Construction of a Line Graph

1st step: Round the data to be shown upto 1 digit of even numbers.

2nd step: Draw X and Y-axis. Mark the time series variables (years/months) on the X axis and the data quantity/value to be plotted on Y axis.

3rd step: Choose an appropriate scale to show data and label it on Y-axis. If the data involves a negative figure then the selected scale should also show it.

4th step: Plot the data to depict year/month-wise values according to the selected scale on Y-axis, mark the location of the plotted values by a dot and join these dots by a free hand drawn line

Construct a line graph to represent the data

Line diagrams are the simplest of all diagrams.

Line graph is most useful in displaying data or information that change continuously over time.

2. Polygraph

Polygraph is a line graph in which two or more than two variables are shown on a same diagram by different lines. It helps in comparing the data. Examples which can be shown as polygraph are:

• The growth rate of different crops like rice, wheat, pulses in one diagram.
• The birth rates, death rates and life expectancy in one diagram.
• Sex ratio in different states or countries in one diagram.

Construction of a Polygraph

All steps of construction of polygraph are similar to that of line graph. But different lines are drawn to indicate different variables.

Construct a polygraph to compare the variables.

3. Bar Diagram

It is also called a columnar diagram. The bar diagrams are drawn through columns of equal width. Following rules were observed while constructing a bar diagram:

(a)  The width of all the bars or columns is similar.

(b)  All the bars should are placed on equal intervals/distance.

(c)  Bars are shaded with colours or patterns to make them distinct and attractive.

Three types of bar diagrams are used to represent different data sets:

• The simple bar diagram
• Compound bar diagram
• Polybar diagram.

Simple Bar Diagram

Construction  of   a simple  bar diagram

A simple bar diagram is constructed for an immediate comparison. It is advisable to arrange the given data set in an ascending or descending order and plot the data variables accordingly. However, time series data are represented according to the sequencing of the time period.

Construction Steps:

Draw X and Y- axes on a graph paper. Take an interval and mark it on Y-axis to plot data. Divide X-axis into equal parts to draw bars. The actual values will be plotted according to the selected scale.

Line and Bar Graph

The line and bar graphs as drawn separately and may also be combined to depict the data related to some of the closely associated characteristics such as the climatic data of mean monthly temperatures and rainfall.

                                        Construct a Line and bar Graph

Construction:

• Draw X and Y-axes of a suitable length and divide X-axis into parts to show months in a year.
• Select a suitable scale with equal intervals on the Y-axis and label it at its right side.
• Similarly, select a suitable scale with equal intervals on the Y-axis and label at its left side.
• Plot data using line graph and columnar diagram.

Multiple Bar Diagram

Multiple bar diagrams are constructed to represent two or more than two variables for the purpose of comparison. For example, a multiple bar diagram may be constructed to show proportion of males and females in the total, rural and urban population or the share of canal, tube well and well irrigation in the total irrigated area in different states.

              Construct a Multiple bar Diagram.

Construction

(a) Mark time series data on X-axis and variable data on Y-axis as per the selected scale.

(b) Plot the data in closed columns.

• Compound Bar Diagram

When different components are grouped in one set of variable or different variables of one component are put together, their representation is made by a compound bar diagram. In this method, different variables are shown in a single bar with different rectangles.

Construct a Compound Bar Diagram

• Arrange the data in ascending or descending order.
• A single bar will depict the set of variables by dividing the total length of the bar as per percentage.

TWO DIMENSIONAL DIAGRAMS

• Pie Diagram

Pie diagram is another diagramatic method of the representation of data. It is drawn to depict the total value of the given attribute using a circle. Dividing the circle into corresponding degrees of angle then represent the sub– sets of the data. Hence, it is also called as Divided Circle Diagram. The angle of each variable is calculated using the following formulae.

Pie Diagram.

If data is given in percentage form, the angles are calculated using the given formulae.

Calculation of Angles:

(a) Arrange the data on percentages in an ascending order.

(b) Calculate the degrees of angles for showing the given values

(b)It could be done by multiplying percentage with a constant of 3.6 as derived by dividing the total number of degrees in a circle by 100,

                        i.  e. 360/100.

(c)Plot the data by dividing the circle into the required number of divisions to show the share different regions/countries

(a)Select a suitable radius for the circle to be drawn. A radius of 3, 4 or 5 cm may be chosen for the given data set.

(b)Draw a line from the centre of the circle to the arc as a radius.

(c)Measure the angles from the arc of the circle for each category of vehicles in an ascending order clock-wise, starting with smaller angle.

(d) Complete the diagram by adding the title, sub – title, and the legend. The legend mark be chosen for each variable/category and highlighted by distinct shades/colours.

Precautions

(a)The circle should neither be too big to fit in the space nor too small to be illegible.

(b) Starting with bigger angle will lead to accumulation of error leading to the plot of the smaller angle difficult.

THREE DIMENSIONAL DIAGRAMS

These diagrams are used when only one point is to be compared and the ratio between the highest and the lowest measurements is more than 100. For these diagrams, the cube root of various measurements is calculated and the side of each cube istaken in proportion to the cube roots

Among the three dimensional diagrams, cubes are the easiest and should be used only in cases where the figures cannot be adequately presented through bar, square or circle diagrams.In case of cubes, all three dimensions, length, width and height are taken into consideration.In case of a cylinder, the length and diameter of circle are taken into consideration. A sphere in the shape of a bell can be used in a three dimensional form.

Pictograph is a way of representing statistical data using symbolic figures to match the frequencies of different kinds of data.A pictogram is another form of pictoral bar chart. Such charts are useful in presenting data to people whocannot understand charts.Small symbols or simple figures are used to represent the size of data.

To construct pictograms, the following suggestions are made;

• The symbols must be simple and clear.
• The quantity represented by the symbol should be given
• Large quantities are shown by increasing the number and not by increasing the size of symbols. A part of symbol can be used to represent a quantity smaller than the whole symbol

Major advantages of pictograms

• First, they are farmore attractive when compared to other diagrams. As such they generate interest in audience.
• Second, it has been observed that the facts presentedby pictograms are remembered for long time than tables, bars and other diagrams.

Limitations of pictograms

• First, they are difficult to draw
• we cannot show the actual data properly

Cartograms are the maps used to present the statistical data on a geographical basis. The various figures in different regions on maps are shown either by

• Shades or colours
• Dots or bars
• Diagrams or pictures
• By putting numerical figures in each geographical area.

CLASSIFIATION

There are three main types of cartograms, each have a very different way of showing attributes of geographic objects-

• Non-contiguous,
• Contiguous and
• Dorling cartograms.

NON-CONTIGUOUS CARTOGRAMS

A non-contiguous cartogram is the simplest and easiest type of cartogram to make. In a non-contiguous cartogram, the geographic objects do not have to maintain connectivity with their adjacent objects. This connectivity is called topology. By freeing the objects from their adjacent objects, they can grow or shrink in size and still maintain their shape. Here is an example of two non-contiguous cartograms.

The cartogram on the left has maintained the object’s centroid (a centroid is the weighted center point of an area object.) Because the object’s center is staying in the same place, some of the objects will begin to overlap when the objects grow or shrink depending on the attribute (in this case population.) In the cartogram on the right, the objects not only shrink or grow, but they also will move one way or another to avoid overlapping with another object.

CONTIGUOUS CARTOGRAMS

In a non-contiguous cartogram topology was sacrificed in order to preserve shape. In a contiguous cartogram, the reverse is true- topology is maintained (the objects remain connected with each other) but this causes great distortion in shape.The cartographer must make the objects the appropriate size to represent the attribute value, but he or she must also maintain the shape of objects as best as possible, so that the cartogram can be easily interpreted. Here is an example of a contiguous cartogram of population in California’s countries. Compare this to the previous non-contiguous cartogram.

DORLING CARTOGRAM

A Dorling cartogram maintains neither shape, topology nor object centroids, though it has proven to be a very effective cartogram method. To create a Dorling cartogram, instead of enlarging or shrinking the objects themselves, the cartographer will replace the objects with a uniform shape, usually a circle, of the appropriate size.

Secondly, the Dorling Cartogram attempts to move the figures the shortest distance away from their true locations

Another Dorling-like cartogram is the Demers Cartogram, which is different in two ways. It uses squares rather than circles; this leaves fewer gaps between the shapes. The Demers cartogram often sacrifices distance to maintain contiguity between figures, and it will also sacrifice distance to maintain certain visual cues (The gap between figures used to represent San Francisco Bay in the Demers Cartogram below is a good example of a visual cue)

PSEUDO-CARTOGRAMS

Pseudo-cartograms (or false cartograms ) are representations that may look like cartograms but do not follow certain cartogram rules. Perhaps the most famous type of pseudo-cartogram was developed by Dr. Waldo Tobler. In this case, instead of enlarging or shrinking the objects themselves, Tobler moves the object’s connections to a reference grid such as latitude or longitude in order to give the same effect. This maintains good directional accuracy in the cartogram (if county A is directly north of county B, it will still remain directly north in the cartogram .Note in previous examples, such as the Dorling Cartogram, this is not always true) however; this is a false cartogram because it creates extensive error in the actual size of the objects

ADVANTAGES OF CARTOGRAMS

• Cartograms are simple and easy to understand.
• They are generally used when the regional or geographical comparisons are to be made.

LIMITATIONS

• Cartograms are very attractive but they should be used especially where geographic comparisons are to be made and where approximate measures can serve the purpose.
• This is understandable as the maps are unable to provide 100% accuracy.

. No single diagram is suited for all practical situations. The choice of a particular diagram for visual presentation of a given set of data is not an easy one and requires great skill, intelligence and expertise. The choice will primarily depend upon the nature of the data and object of the presentation, i.e., the type of the audience to whom the diagrams are to be presented and it should be made with utmost care and caution. A wrong or  injudicious selection of the diagram will distort the true characteristics of the phenomenon to be presented and might lead to very wrong and misleading interpretations.

• https://gradestack.com/Class-11th-Commerce/Presentation-of-Data/Diagrammatic-Presentation/17643-3574-27365-study-wtw
• http://www.economicsdiscussion.net/statistics/data/graphical-representation-of-statistical-data/12010
• https://www.scribd.com/doc/41044016/Diagrammatic-Graphical-Presentation-of-Data
• http://www.publishyourarticles.net/knowledge-hub/statistics/diagrammatic-presentation-of-data/1103/
• https://www.youtube.com/watch?v=2TMs4-hIA04

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

Scientific Method

8. data: using graphs and visual data.

Flip through any scientific journal or textbook and you’ll notice quickly that the text is interspersed with graphs and figures. In some journals, as much as 30% of the space is taken up by graphs (Cleveland, 1984), perhaps surpassing the adage that “a picture is worth a thousand words.” Although many magazines and newspapers also include graphs, the visual depiction of data is fundamental to science and represents something very different from the photographs and illustrations published in magazines and newspapers. Although numerical data are initially compiled in tables or databases, they are often displayed in a graphic form to help scientists visualize and interpret the variation, patterns, and trends within the data.

Data lie at the heart of any scientific endeavor. Scientists in different fields collect data in many different forms, from the magnitude and location of earthquakes , to the length of finch beaks, to the concentration of carbon dioxide in the atmosphere and so on. Visual representations of scientific data have been used for centuries – in the 1500s, for example, Copernicus drew schematic sketches of planetary orbits around the sun – but the visual presentation of numerical data in the form of graphs is a more recent development.

Using graphs to present numerical data

In 1786, William Playfair, a Scottish economist, published The Commercial and Political Atlas , which contained a variety of economic statistics presented in graphs. Among these was the image shown in Figure 1, a graph comparing exports from England with imports into England from Denmark and Norway from 1708 to 1780 (Playfair, 1786). (Incidentally, William Playfair was the brother of John Playfair, the geologist who elucidated James Hutton ‘s fundamental work on geological processes to the broader public. To learn more, see our module The Rock Cycle: Uniformitarianism and Recycling .)

Playfair’s graph displayed a powerful message very succinctly. The graph shows time on the horizontal (x) axis and money in English pounds on the vertical (y) axis. The yellow line shows the monetary value of imports to England from Denmark and Norway; the red line shows the monetary value of exports to Denmark and Norway from England. Although a table of numerical data would show the same information, it would not be immediately apparent that something important happened in about 1753: England began exporting more than it imported, placing the “balance in favour of England.” This simple visualization of a large numerical dataset made it easy to comprehend quickly.

Graphs and figures quickly became standard components of science and scientific communication, and the use of graphs has increased dramatically in scientific journals in recent years, almost doubling from an average of 35 graphs per journal issue to more than 60 between 1985 and 1994 (Zacks et al., 2002). This increase has been attributed to a number of causes, including the use of computer software programs that make producing graphs easy, as well as the production of increasingly large and complex datasets that require visualization to be interpreted.

Graphs are not the only form of visualized data , however – maps, satellite imagery, animations, and more specialized images like atomic orbital depictions are also composed of data, and have also become more common. Creating, using, and reading visual forms of data is just one type of data analysis and interpretation (see our Data Analysis and Interpretation module), but it is ubiquitous throughout all fields and methods of scientific investigation.

Comprehension Checkpoint

Representing data graphically

• means taking a photograph.
• makes it easier to interpret complex datasets.

Interpreting graphs

The majority of graphs published in scientific journals relate two variables . As many as 85% of graphs published in the journal Science , in fact, show the relationship between two variables, one on the x-axis and another on the y-axis (Cleveland, 1984). Although many other kinds of graphs exist, knowing how to fully interpret a two-variable graph can not only help anyone decipher the vast majority of graphs in the scientific literature but also offers a starting point for examining more complex graphs. As an example, imagine trying to identify any long-term trends in the data table that follows of atmospheric carbon dioxide concentrations taken over several years at Mauna Loa (Table 1; click on the excerpt below to see the complete data table).

The variables are straightforward – time in months in the top row of the table, years in the far left column of the table, and carbon dioxide (CO 2 ) concentrations within the individual table cells . Yet, it is challenging for most people to make sense of that much numerical information. You would have to look carefully at the entire table to see any trends. But if we take the exact same data and plot it on a graph, this is what it looks like (Figure 2):

Reading a graph involves the following steps:

Describing the graph: The x-axis shows the variable of time in units of years, and the y-axis shows the range of the variable of CO 2 concentration in units of parts per million (ppm). The dots are individual measurements of concentrations – the numbers shown in Table 1. Thus, the graph is showing us the change in atmospheric CO 2 concentrations over time.

Describing the data and trends: The line connects consecutive measurements, making it easier to see both the short- and long-term trends within the data. On the graph, it is easy to see that the concentration of atmospheric CO 2 steadily rose over time, from a low of about 315 ppm in 1958 to a current level of about 375 ppm. Within that long-term trend, it’s also easy to see that there are short-term, annual cycles of about 5 ppm.

Making interpretations: On the graph, scientists can derive additional information from the numerical data, such as how fast CO 2 concentration is rising. This rate can be determined by calculating the slope of the long-term trend in the numerical data, and seeing this rate on a graph makes it easily apparent. While a keen observer may have been able to pick out of the table the increase in CO 2 concentrations over the five decades provided, it would be difficult for even a highly trained scientist to note the yearly cycling in atmospheric CO 2 in the numerical data – a feature elegantly demonstrated in the sawtooth pattern of the line.

Putting data into a visual format is one step in data analysis and interpretation , and well-designed graphs can help scientists interpret their data. Interpretation involves explaining why there is a long-term rise in atmospheric CO 2 concentrations on top of an annual fluctuation, thus moving beyond the graph itself to put the data into context. Seeing the regular and repeating cycle of about 5 ppm, scientists realized that this fluctuation must be related to natural changes on the planet due to seasonal plant activity. Visual representation of these data also helped scientists to realize that the increase in CO 2 concentrations over the five decades shown occurs in parallel with the industrial revolution and thus are almost certainly related to the growing number of human activities that release CO 2 (IPCC, 2007).

It is important to note that neither one of these trends (the long-term rise or the annual cycling) nor the interpretation can be seen in a single measurement or data point. That’s one reason why you almost never hear scientists use the singular of the word data – datum. Imagine just one point on a graph. You could draw a trend line going through it in any direction. Rigorous scientific practice requires multiple data points to make a clear interpretation, and a graph can be critical not only in showing the data themselves, but in demonstrating on how much data a scientist is basing his or her interpretation.

We just followed a short, logical process to extract a lot of information from this graph. Although an infinite variety of data can appear in graphical form, this same procedure can apply when reading any kind of graph. To reiterate:

• Describe the graph: What does the title say? What variable is represented on the x-axis? What is on the y-axis? What are the units of measurement? What do the symbols and colors mean?
• Describe the data: What is the numerical range of the data? What kinds of patterns can you see in the distribution of the data as they are plotted?
• Interpret the data: How do the patterns you see in the graph relate to other things you know?

The same questions apply whether you are looking at a graph of two variables or something more complex. Because creating graphs is a form of data analysis and interpretation , it is important to scrutinize a scientist’s graphs as much as his or her written interpretation.

Graphs are important because they

• can make trends and patterns in the data clear.
• show one piece of data clearly.

Error and uncertainty estimation in visual data

Graphs and other visual representations of scientific information also commonly contain another key element of scientific data analysis – a measure of the uncertainty or error within measurements (see our Uncertainty, Error, and Confidence module). For example, the graph in Figure 3 presents mean measurements of mercury emissions from soil at various times over the course of a single day. The error bars on each vertical bar provide the standard deviation of each measurement. These error bars are included to demonstrate that the change in emissions with time are greater than the inherent variability within each measurement (see our Statistics in Science module for more information).

Graphical displays of data can also be used not just to display error, but to quantify error and uncertainty in a system . For example, Figure 4 shows a gas chromatograph of a fuel oil spill. Peaks in the chromatograph (the blue line) provide information about the chemicals identified in the spill, and the peak size can provide an estimate of the relative concentration of that specific chemical in the spill. However, before this information can be extracted from the graph, instrument error and uncertainty must be calculated (the red line) and subtracted from the peak area. As you can see in Figure 4, instrument variability decreases as you move from left to right in the graph, and in this case, the graphical display of the error is therefore critical to accurate analysis of the data.

Graphical displays of data are used to ___________ error.

• display and quantify
• conceal or hide

Misuse of scientific images

Poor use of graphics can highlight trends that don’t really exist, or can make real trends disappear. Some have tried to point out errors with the now widely accepted notion of climate change by using misleading graphics. Figure 5, below, is one such graphic that has appeared in print. The point drawn by the creator of this is that the bottom graph, which shows relatively little change in temperature over the past 1,000 years, disputes the top graph used by the Intergovernmental Panel on Climate Change that shows a recent, rapid temperature increase.

At first glance the bottom graph does seem to contradict the top graph. However, looking more closely you realize:

• The two graphs actually represent completely different datasets . The top graph is a representation of change in annual mean global temperature normalized to a 30-year period, 1960-1990, whereas the bottom graph represents average temperatures in Europe compared to an average over the 20th-century.
• In addition, the y-axes of the two graphs are displayed on differing scales – the bottom graph has more space between the 0.5° lines.

Both of these techniques tend to exaggerate the variability in the lower graph. However, the primary reason for the difference in the graphs is not actually shown in the graphs. The author of the graphic created the image on the bottom using different calculations that did not take into account all of the variables that climate scientists used to create the top graph. In other words, the graphs simply do not show the same data .

These are common techniques used to distort visual forms of data – manipulating axes, changing one of the variables in a comparison, changing calculations without full explanation – that can obscure a true comparison.

Visualizing spatial and three-dimensional data

There are other kinds of visual data aside from graphs. You might think of a topographic map or a satellite image as a picture or a sketch of the surface of the earth, but both of these images are ways of visualizing spatial data. A topographic map shows data collected on elevation and the location of geographic features like lakes or mountain peaks (see Figure 6). These data may have been collected in the field by surveyors or by looking at aerial photographs, but nonetheless the map is not a picture of a region – it is a visual representation of data. The topographic map in Figure 6 is actually accomplishing a second goal beyond simply visualizing data: It is taking three-dimensional data (variations in land elevation) and displaying them in two dimensions on a flat piece of paper.

Likewise, satellite images are commonly misunderstood to be photographs of the Earth from space, but in reality they are much more complex than that. A satellite records numerical data for each pixel, and it does so at certain predefined wavelengths in the electromagnetic spectrum (see our Light II: Electromagnetism module for more information). In other words, the image itself is a visualization of data that has been processed from the raw data received from the satellite. For example, the Landsat satellites record data in seven different wavelengths: three in the visible spectrum and four in the infrared wavelengths. The composite image of four of those wavelengths is displayed in the image of a portion of the Colorado Rocky Mountains shown in Figure 7. The large red region in the lower portion of the image is not red vegetation in the mountains; instead, it is a region with high values for emission of infrared (or thermal) wavelengths. In fact, this region was the site of a large forest fire, known as the Hayman Fire, a month prior to the acquisition of the satellite image in July 2002.

What do satellite images and topographic maps have in common?

• They are visual representations of data.
• They are photographs of a place.

Working with image-based data

The advent of satellite imagery vastly expanded one data collection method: extracting data from an image. For example, from a series of satellite images of the Hayman Fire acquired while it was burning, scientists and forest managers were able to extract data about the extent of the fire (which burned deep into National Forest land where it could not be monitored by people on the ground), the rate of spread, and the temperature at which it was burning. By comparing two satellite images, they could find the area that had burned over the course of a day, a week, or a month. Thus, although the images themselves consist of numerical data, additional information can be extracted from these images as a form of data collection.

Another example can be taken from the realm of atomic physics. In 1666, Sir Isaac Newton discovered that when light from the sun is passed through a prism, it separates into a characteristic rainbow of light. Almost 200 years after Newton, John Herschel and W. H. Fox Talbot demonstrated that when substances are heated and the light they give off is passed through a prism, each element gives off a characteristic pattern of bright lines of color, but they did not understand why (see Figure 8). In 1913, the Danish physicist Niels Bohr used these images to make a startling proposal: He suggested that the line spectra of elements were due to the movement of electrons between different orbitals, and thus these spectra could provide information regarding the electron configuration of the elements (see our Atomic Theory II: Ions, Isotopes, and Electron Shells module for more information). You can actually calculate the potential energy difference between electron orbitals in atoms by analyzing the color (and thus wavelength) of light emitted.

Photographs and videos are also visual data . In 2005, a group of scientists based in part at the Cornell Ornithology lab published their findings that a bird believed to be extinct in North America, the Ivory-billed Woodpecker, had been spotted in Arkansas (Fitzpatrick et al., 2005). Their primary evidence consisted of video footage and photographs of a bird in flight, which they included in their paper along with a detailed analysis of the features of the images and video that suggested that the bird was an Ivory-billed Woodpecker. (You can read the article and see the photographs here .)

Graphs for scientific communication

Many areas of study within science have more specialized graphs used for specific kinds of data . Evolutionary biologists, for example, use evolutionary trees or cladograms to show how species are related to each other, what characteristics they share, and how they evolve over time. Geologists use a type of graph called a stereonet that represents the inside of a hemisphere in order to depict the orientation of rock layers in three-dimensional space. Many fields now use three-dimensional graphs to represent three variables , though they may not actually represent three-dimensional space.

Regardless of the exact type of graph, the creation of clear, understandable visualizations of data is of fundamental importance in all branches of science. In recognition of the critical contribution of visuals to science, the National Science Foundation and the American Association for the Advancement of Science sponsor an annual Science and Engineering Visualization Challenge, in which submissions are judged based on their visual impact, effective communication, and originality (NSF, 2007). Likewise, reading and interpreting graphs is a key skill at all levels, from the introductory student to the research scientist. Graphs are a key component of scientific research papers, where new data are routinely presented. Presenting the data from which conclusions are drawn allows other scientists the opportunity to analyze the data for themselves, a process whose purpose is to keep scientific experiments and analysis as objective as possible. Although tables are necessary to record the data, graphs allow readers to visualize complex datasets in a simple, concise manner.

Understanding graphs and other visual forms of data is an important skill for scientists. This module describes how to read and interpret graphs and introduces other types of visual data. With a look at various examples, it is clear how trends can be grasped easily when the data is shown in a visual form.

Key Concepts

• Visual representations of data are essential for both data analysis and interpretation.
• Visualization highlights trends and patterns in numeric datasets that might not otherwise be apparent.
• Understanding and interpreting graphs and other visual forms of data is a critical skill for scientists and students of science.

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• Diagrammatic Presentation of Data

Nowadays a lot of emphases is laid upon exceptional presentation of data.  All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts etc.

Suggested Videos

Bar diagrams.

As the name suggests, when data is presented in form of bars or rectangles , it is termed to be a bar diagram.

Features of a Bar

• The rectangular box in a bar diagram is known as a bar. It represents the value of a variable .
• These bars can be either vertically or horizontally arranged.
• Bars are equidistant from each other.
• Each bar originates from a common baseline or a common axis.
• The width of bars remain same but the height changes, according to the value of a variable, to denote the difference between their values.
• Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

Browse more Topics under Presentation Of Data

• Textual and Tabular Presentation of Data

Types of Bar Diagrams

Simple bar diagram.

These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of variable whereas the X-axis contains divisions for entities like years, time periods, areas etc.

Multiple Bar Diagram

Unlike single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates etc.

Separate sets of numerical data are differentiated with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

Sub-divided or Differential Bar Diagrams

Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent same values as in simple and multiple bar diagrams.

Percentage Bar Diagrams

This is derived further from the subdivided bar diagrams. In this, each bar has the same height that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

Deviation Bar Diagrams

Lastly, the deviation bar diagrams are most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of contributions of each part. The steps for construction of a pie diagram are:

The first step involves finding out respective percentages. This is done by a simple mathematical formula to find out percentages which is –

{(Parts for the respective sector)/total parts) ×100} .

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows:

(30/100) × 100= 30%

(20/100) × 100= 20%

(50/100) × 100= 50%

2] A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)×360°

3] Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

A Solved Example for You

Q:   Which among the following is not a feature of a bar in the bar diagram?

• The width is same but the heights are generally different
• They are rectangular in shape
• Bars should not be equidistant
• Each bar originates from a common baseline

Ans:   Of all the above options, option C is incorrect because conventionally the bars should be equidistant.

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18 Types of Diagrams You Can Use to Visualize Data (Templates Included)

Have you ever found yourself stuck while trying to explain a complex concept to someone? Or struggling to put your idea into words?

This is where diagrams come in.

While simple text is best for highlighting figures or information, diagrams are handy for conveying complex ideas and loads of information without overwhelming your audience. They can visualize almost anything, from numerical data to qualitative relationships, making them versatile tools in numerous fields.

Whether you’re in the academe or enterprise setting, this guide is for you. We’ll explore the different types of diagrams with a brief explanation for each type, the best time to use a diagram type, and how you can use them to be a better visual storyteller and communicator. You’ll also find examples and templates for each type of diagram.

Let’s get on with it.

You can also follow along by creating a free account . Select a template to get started.

What exactly is a diagram? 

A diagram is a visual snapshot of information. Think of diagrams as visual representations of data or information that communicate a concept, idea, or process in a simplified and easily understandable way. You can also use them to illustrate relationships, hierarchies, cycles, or workflows. 

Diagrams aren’t just used to show quantitative data, such as sales earnings or satisfaction ratings with a diagram. They’re equally helpful if you want to share qualitative data. For example, a diagram could be used to illustrate the life cycle of a butterfly, showcasing each transformation stage. 

Now, let’s jump into the various types of diagrams, ranging from simple flow charts to the more complex Unified Modeling Language (UML) diagrams.

18 diagram types and when to use each type 

Whether you’re doing data analysis or need a simple visual representation of data, there is a wide array of diagrams at your fingertips. If you’re having a hard time choosing the right diagram for your data visualization needs, use the list below as a quick guide. 

1. Flowchart 

A flowchart is a type of diagram that acts as a roadmap for a process or workflow. It uses shapes and arrows to guide you through each step, making complex procedures simple to understand.

Flowcharts are best for : Simplifying complex processes into understandable stages, making it easier for your readers to follow along and see the ‘big picture”. 

2. Line graph

Line graphs , sometimes called line charts, visualizes numerical data points connected by straight lines. In a line graph or line chart, data points representing different time periods are plotted and connected by a line. This helps with easy visualization of trends and patterns.

Line graphs are best for: Representing the change of one or more quantities over time, making them excellent for tracking the progression of data points.

3. Bar chart 

A bar chart , often interchangeable with bar graphs, is a type of diagram used primarily to display and compare data. For this diagram type, rectangular bars of varying lengths represent data of different categories or groups. Each bar represents a category, and the length or height of the bar corresponds to the numeric data or quantity.

Variations of bar charts include stacked bar charts, grouped bar charts, and horizontal bar charts. 

Bar charts are best for : Comparing the frequency, count, or other measures (such as average) for different categories or groups. A bar chart is particularly useful if you want to display data sets that can be grouped into categories.

4. Circle diagram or pie chart

A pie chart is a circular diagram that represents data in slices. Each slice of the pie chart represents a different category and its proportion to the whole.

Pie charts are best for: Displaying categorical data where you want to highlight each category’s percentage of the total.

5.Venn diagrams

A Venn diagram compares the differences and similarities of groups of things. As a diagram based on overlapping circles, each circle in a Venn diagram represents a different set, and their overlap represents the intersection of the data sets. 

Venn diagrams are best for : Visualizing the relationships between different groups of things. They are helpful when you want to show areas of overlap between elements. A good example is if you want to compare the features of different products or two overlapping concepts, like in the Ikigai Venn diagram template below. Easily create your Venn diagram with Piktochart’s online Venn diagram maker .

6. Tree diagrams

A tree diagram is a diagram that starts with one central idea and expands with branching lines to show multiple paths, all possible outcomes, decisions, or steps. Each ‘branch’ represents a possible outcome or decision in a tree diagram, moving from left to right. Tree diagrams are best for : Representing hierarchy like organizational roles, evolutionary relationships, or possible outcomes of events like when a company launches a product. 

7. Organizational chart 

Organizational charts are diagrams used to display the structure of an organization. In an organizational chart, each box or node represents a different role or department, and lines connecting the boxes illustrate the lines of authority, communication, and responsibility. The chart typically starts with the highest-ranking individual or body (like a CEO or Board of Directors) at the top and branches downwards to various levels of management and individual employees.

Organizational charts are best for : Showing relationships between different members and departments in a company or organization. 

8. Gantt charts 

Gantt charts are typically used in project management to represent the timeline of a project. They consist of horizontal bars, with each bar representing a task or activity.

For this type of diagram, each chart is represented by a horizontal bar spanning from its start date to its end date. The length of the bar corresponds to the duration of the task. Tasks are listed vertically, often in the order they need to be completed. In some projects, tasks are grouped under larger, overarching activities or phases.

Gantt charts are best for : Projects where you need to manage multiple tasks that occur over time, often in a specific sequence, and may depend on each other.

9. Unified Modeling Language (UML) diagram

Software engineers use Unified Modeling Language (UML) diagrams to create standardized diagrams that illustrate the building blocks of a software system.

UML diagrams, such as class diagrams, sequence diagrams, and state diagrams, provide different perspectives on complex systems. Class diagrams depict a system’s static structure, displaying classes, attributes, and relationships. Meanwhile, sequence diagrams illustrate interactions and communication between system entities, providing insight into system functionality. 

UML diagrams are best for : Visualizing a software system’s architecture in software engineering.

10. SWOT analysis diagrams 

A SWOT analysis diagram is used in business strategy for evaluating internal and external factors affecting the organization. The acronym stands for Strengths, Weaknesses, Opportunities, and Threats. Each category is represented in a quadrant chart, providing a comprehensive view of the business landscape.

SWOT diagrams are best for : Strategic planning and decision-making. They represent data that can help identify areas of competitive advantage and inform strategy development.

Piktochart offers professionally-designed templates to create diagrams , reports , presentations , brochures , and more. Sign up for a free account today to create impressive visuals within minutes.

11. Fishbone diagram 

Fishbone diagrams, sometimes called cause-and-effect diagrams,  are used to represent the causes of a problem. They consist of a central idea, with different diagrams or branches representing the factors contributing to the problem.

Fishbone diagrams are best for : Brainstorming and problem-solving sessions.

12. Funnel chart

A funnel chart is a type of diagram used to represent stages or progress. In a funnel chart, each stage is represented by a horizontal bar, and the length of the bar corresponds to the quantity or value at that stage. The chart is widest at the top, where the quantity or value is greatest, and narrows down to represent the decrease at each subsequent stage.

Funnel charts are best for: Visual representation of the sales pipeline or data visualization of how a broad market is narrowed down into potential leads and a select group of customers.

13. SIPOC diagrams

A SIPOC diagram is used in process improvement to represent the different components of a process. The acronym stands for Suppliers, Inputs, Process, Outputs, and Customers.

SIPOC diagrams are best for: Providing a high-level view of a process which helps visualize the sequence of events and their interconnections.

14. Swimlane diagrams

Swimlane diagrams are best for mapping out complex processes that involve multiple participants or groups.

Keep in mind that each lane (which can be either horizontal or vertical) in a swimlane diagram represents a different participant or group involved in the process. The steps or activities carried out by each participant are plotted within their respective lanes. This helps clarify roles and responsibilities as well as the sequence of events and points of interaction.

Swimlane diagrams are best for : Visualizing how different roles or departments interact and collaborate throughout a workflow or process.

15. Mind maps

A mind map starts with a central idea and expands outward to include supporting ideas, related subtopics, concepts, or tasks, which can be further subdivided as needed. The branches radiating out from the central idea represent hierarchical relationships and connections between the different pieces of information in a mind map.

Mind maps are best for : Brainstorming, taking notes, organizing information, and visualizing complex concepts in a digestible format.

16. Scatter Plots

Scatter plots are used to compare data and represent the relationship between two variables. In a scatter plot, each dot represents a data point with its position along the x and y axes representing the values of two variables.

Scatter plots are best for : Observing relationships and trends between the two variables. These scatter plots are useful for regression analysis, hypothesis testing, and data exploration in various fields such as statistics, economics, and natural sciences.

17. PERT chart

PERT (Project Evaluation Review Technique) charts are project management tools used to schedule tasks. Each node or arrow represents each task, while lines represent dependencies between tasks. The chart includes task duration and earliest/latest start/end times.

Construction project managers often use PERT charts to schedule tasks like design, site prep, construction, and inspection. Identifying the critical path helps focus resources on tasks that impact the project timeline.

PERT charts are best for : Visualizing the sequence of tasks, the time required for each task, and project timelines.

18. Network diagrams

A network diagram visually represents the relationships between elements in a system or project. In network diagrams, each node represents an element, such as a device in a computer network or a task in a project. The lines or arrows connecting the nodes represent the relationships or interactions between these elements.

Network diagrams are best for: Visually representing the relationships or connections between different elements in a system or a project. They are often used in telecommunications, computer networking, project management, and organization planning.

Choosing the right diagram starts with a good understanding of your audience

Understanding your audience’s needs, expectations, and context is necessary before designing diagrams. The best diagram is not the one that looks the most impressive but the one that communicates complex information most clearly and effectively to your intended audience.

Make professional diagrams for free with no design experience with Piktochart’s online diagram maker . Sign up for free .

Kyjean Tomboc is an experienced content marketer for healthcare, design, and SaaS brands. She also manages content (like a digital librarian of sorts). She lives for mountain trips, lap swimming, books, and cats.

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Diagrammatic Presentation Of Data

Introduction.

The diagrammatic representation also helps in having a bird’s eye view or overall view of the differentiation of data. It is a norm to present statistical data in the form of diagrams so that it becomes easier to comprehend and understand them. Therefore, diagrammatic representation is an important tool in statistics.

What is a Diagrammatic Presentation of Data?

Diagrammatic representation refers to a representation of statistical data in the form of diagrams. The diagrams used in representing statistical data are geometrical figures, such as lines, bars, and circles. The intention of using geometrical figures in statistical presentation is to make the study more interesting and easy to understand. Diagrammatic representations are widely used in statistics, economics, and many other fields of study.

Types of Diagrammatic Presentations of Data

Various types of diagrammatic representations of data depend on the dataset and the particular statistical elements in them. Data presentation can be made in different types and forms.

These can be broadly classified into the following one-dimensional types −

Line Diagram

In a line diagram, straight lines are used to indicate various parameters. Here, a line represents the sequence of data associated with the changing of a particular variable.

Properties of Line Diagram −

The Lines are either in vertical or horizontal directions.

There may be uniform scaling but this is not mandatory.

The lines that connect the data points offer the statistical representation of data.

The following is an example of a line diagram that shows profits in Rs crore from 2002 till 2008. Profit in 2002 was Rs 5 Crore while in 2008 it was Rs 24 Crore.

Bar Diagram

Bar diagrams have rectangular shapes of equal width that represent statistical data in a straightforward manner. Bar diagrams are one of the most widely used diagrammatic representations.

Properties of Bar Diagram −

The Bars can be vertical or horizontal in directions.

All bars in a diagram have a uniform width.

All the Bars have a common and same base.

The height or width of the Bar shows the required value.

The following is an example of a Bar Chart that has time on the X axis and profits on the Y axis.

Also known as a "circle chart" , the pie chart divides the circular statistical graphic into sectors or sections to illustrate the numerical data. Each sector in the circle denotes a proportionate part of the whole. Pie-chart works the best at the time when we want to denote the composition of something. In most cases, the pie chart replaces other diagrammatic representations, such as the bar graph, line plots, histograms, etc.

In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

Advantages of Diagrammatic Presentation of Data

Easier to understand.

Pictorial representations are usually easier to understand than statistical text or representation in tabular form. One can easily understand which portion or part has more contribution toward the overall dataset. This helps in understanding the data better.

The creators of diagrams usually keep the simplicity of presentation in mind to offer more information to readers. That is why diagrams are easier to comprehend than texts and tables.

More attractive

Pictorial or diagrammatic representations of datasets are more attractive than normal representations. As colors and various other tools can be incorporated into diagrams, they become more attractive and comprehensible for the readers.

Moreover, as diagrams can be made more interactive with the help of computer graphics, they have become more acceptable and attractive currently.

Simpler presentations

Data can be presented more simply in diagrammatic form. Both extensive unstable data and smaller complex data can be represented by diagrammatic representations more easily. This helps statisticians offer more value to their findings.

Comparison is easier

When two or more data are compared, it is easier to do so in pictorial form. As diagrams clearly show the portion of data consumed, it can be easily understood from the diagrams which part of the data is consuming more area in the diagrams. This can help one to understand the real differences through pictorial comparison.

Universal acceptance

Diagrammatic representation of data is used in many fields of study, such as statistics, science, commerce, economics, etc. So, the diagrams are accepted universally and hence are used everywhere.

Moreover, since there are the same procedures for forming diagrams, the representations mean the same thing to everyone. So, there is nothing to alter when we obtain the diagrams to check the real values. It helps analysts solve problems universally.

Improvement in presentation

Diagrammatic representations improve the overall representation of data to a large extent. As the data is classified into several groups and presented in a systematic manner in diagrams, the whole presentation of data gets improved during the diagrammatic representation.

Moreover, as diagrams can be made more interactive than texts or tables, diagrammatic presentations are one step ahead in presenting the data in a simpler yet recognizable manner.

More organized and classified data

To represent data in diagrams, they must be organized and classified into comprehensive categories. This helps the data to be organized in a given fashion which makes them orderly and creates a sequence. This in turn helps realize diagrammatic data better than text forms.

Relevance Diagrammatic Presentation of Data

Diagrams are a great way of representing data because they are visually attractive and they can make large, complex datasets look simpler. The otherwise heavy data can be simply and easily represented by line and bar diagrams, and pie charts. This makes data organization simpler and neater.

Moreover, as data must be classified before representation, one must organize them according to the norms required. So, diagrammatic representations save lots of time and resources.

Diagrams also have universal acceptance and so can be used to express data in different forms. This provides the analysts and researchers flexibility to present data in any required form.

Diagrams also remove confusion and offer a simpler tactic to present data. As no special skill has to be learned to represent data in diagrams, they can be used by most to show statistical data and results of various types of research and experiments.

Therefore, diagrammatic representation has great relevance that can be used for the benefit of economists, statisticians, marketing analysts, and a lot of other professionals.

The diagrams are a central part of statistics and their importance can be known from the fact that almost all statistical researchers use them in one way or the other. The diagrammatical representations make inferring statistical data much simpler and easier. It is a much easier way to visualize and understand data in simpler forms too.

To represent data in diagrammatic form, only a simple understanding of Mathematics is required. So, no special skills are needed to use diagrams and this makes them very popular tools for the representation of data sets. Learning how to present data in diagrams, therefore, should be a priority for everyone.

Q1. Which is the simplest diagrammatic presentation of data?

Ans. The simplest diagrammatic presentation of data is a line diagram that shows data in terms of straight lines.

Q2. What are the two characteristics of bar diagrams?

Ans. Bar diagrams have uniform width and their base remains the same.

Q3. How are the sections in a pie chart formed?

Ans. In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

For example, if a section requires 25% of the presentation, it will consume  degrees on the chart.

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6 Conclusion

In this course, you have been introduced to a number of ways of representing data graphically and of summarizing data numerically. We began by looking at some data sets and considering informally the kinds of questions they might be used to answer.

An important first stage in any assessment of a collection of data, preceding any numerical analysis, is to represent the data, if possible, in some informative diagrammatic way. Useful graphical representations that you have met in this course include pie charts, bar charts, histograms and scatterplots. Pie charts and bar charts are generally used with categorical data, or with numerical data that are discrete (counted rather than measured). Histograms are generally used with continuous (measured) data, and scatterplots are used to investigate the relationship between two numerical variables (which are often continuous but may be discrete). You have seen that a transformation may be useful to aid the representation of data.

However, most diagrammatic representations have some disadvantages. In particular, pie charts are hard to assess unless the data set is simple, with a restricted number of categories. Histograms need a reasonably large data set. They are also sensitive to the choice of cutpoints and the widths of the classes.

Numerical summaries of data are very important. You have been introduced to two main pairs of statistics for assessing location and dispersion. The principal measures of location that have been discussed are the mean and the median, and the principal measures of dispersion are the interquartile range and the standard deviation (together with a related measure, the variance). Because of the way they are calculated, these measures ‘go together’ in pairs – the median with the interquartile range, the mean with the standard deviation. The median and interquartile range are more resistant than are the mean and standard deviation; that is, they are less affected by one or two unusual values in a data set.

The mode has also been introduced. The term ‘mode’ is used for the most frequently occurring value in a set of categorical data, as well as to describe a clear peak in the histogram of a set of continuous data.

You have learned about the terms used to describe lack of symmetry in a data set. A data set is said to be right-skew or positively skewed if a histogram (or bar chart, for numerical discrete data) has a relatively large and long tail towards the higher values, on the right of the diagram. The terms left-skew and negatively skewed are used when there is a relatively long tail towards the lower values, on the left of the diagram. Note that the direction of the tail, and not the direction of the main concentration of the data values, is used to describe the skewness. The sample skewness, which is a numerical summary measure of skewness, has also been defined.

Question and Answer forum for K12 Students

Diagrammatic Presentation of Data: Bar Diagrams, Pie Charts etc.

The compilation of this Presentation of Data  Notes makes students exam preparation simpler and organised.

Diagrammatic Presentation of Data

Nowadays a lot of emphasis is laid upon exceptional presentation of data. All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts, etc.

Bar Diagrams

As the name suggests, when data is presented in form of bars or rectangles, it is termed to be a bar diagram.

Features of a Bar

• The rectangular box in a bar diagram is known as a bar. It represents the value of a variable.
• These bars can be either vertically or horizontally arranged.
• Bars are equidistant from each other.
• Each bar originates from a common baseline or a common axis.
• The width of bars remains the same but the height changes, according to the value of a variable, to denote the difference between their values.
• Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

Types of Bar Diagrams

Simple Bar Diagram These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of the variable whereas the X-axis contains divisions for entities like years, time periods, areas, etc.

Multiple Bar Diagram Unlike a single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates, etc.

Separate sets of numerical data are differentiated with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on the Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

Sub-divided or Differential Bar Diagrams Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent the same values as in simple and multiple bar diagrams.

Percentage Bar Diagrams This is derived further from the subdivided bar diagrams. In this, each bar has the same height that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

Deviation Bar Diagrams Lastly, the deviation bar diagrams are the most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of the contributions of each part. The steps for the construction of a pie diagram are:

1. The first step involves finding out the respective percentages. This is done by a simple mathematical formula to find out percentages which are–

{(Parts for the respective sector)/total parts) × 100}.

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows: (30/100) × 100 = 30% (20/100) × 100 = 20% (50/100) × 100 = 50%

2. A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)×360°

3. Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

Question: Which among the following is not a feature of a bar in the bar diagram? A. The width is the same but the heights are generally different B. They are rectangular in shape C. Bars should not be equidistant D. Each bar originates from a common baseline Answer: Of all the above options, option “C” is incorrect because conventionally the bars should be equidistant.

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Introduction - Diagrammatic Presentation of Data

Diagrams are an essential operational tool for the presentation of statistical data. They are objects, mainly geometrical figures such as lines, circles, bars, etc. Statistics elaborated with the help of diagrams make it easier and simpler, thereby enhancing the representation of any type of data.

What is Diagrammatic Representation of Data?

Representation of data assisted by diagrams to increase the simplicity of the statistics surrounding the concerned data is defined as a diagrammatic representation of data. These diagrams are nothing but the use of geometrical figures to improve the overall presentation and offer visual assistance for the reader. 

What are the Types of Diagrams used in Data Presentation?

The type of diagram suitable for data presentation solely depends on the particular dataset and its statistical elements. There are multiple types of diagrams used in data presentation. They can be broadly categorized in the following types of one-dimensional diagrams –

A. Line Diagram

Line diagram is used to represent specific data across varying parameters. A line represents the sequence of data connected against a particular variable. 

Properties of Line Diagram –

The Lines can be used in vertical and horizontal directions.

They may or may not have uniform scaling 

The line connecting the data points state the statistical representation of data.

Example: Arjun, Sayak and Mainak started monitoring their time of reporting for duty for a certain week. A-Line diagram to represent their observed data on average reporting time for those days would look like –

(Image will be Uploaded Soon)

So, as per the Line Diagram, it can be easily determined that Arjun reported for work mostly at 9:30 AM while Sayak and Mainak’s most frequent times of entry at work is 10:30 AM and 10:50 AM respectively. 

B. Bar Diagram

Bar Diagram is used mostly for the comparison of statistical data. It is one of the most straightforward representations of data with the use of rectangular objects of equal width.

Properties of Bar Diagram –

The Bars can be used in vertical and horizontal directions.

These Bars all have a uniform width.

All the Bars have a common base.

The height of the Bar usually corresponds to the required value.

Example: A dataset comparing the percentile marks obtained by Shreyasi and Monika in Science subjects in the examination can be represented with the help of a Bar diagram as –

From this diagram, we can easily compare the percentile marks obtained by Shreyasi and Monika in the subjects Mathematics, Physics, Chemistry and Computer Science. 

C. Pie Chart

To know what a Pie Diagram is, it is advised to brush up on the fundamentals of the geometrical theories and formula of a Circle. For the statistical representation of data, the sectors of a circle are used as the data points of a particular dataset. A sector is the area of a circle formed by the several divisions done by the radii of the same circle.

Example: In a recent survey, a dataset was created to figure how many participants of the survey thought that Tenure or Tenor is the correct spelling in the field of Banking . A Pie Chart would present the collected data as –

With the help of this Pie Chart, it can be easily determined that the percentage of participants in the survey who chose ‘Tenor’, to be the correct spelling of the word for use in the field of banking, is 25% whereas 45% picked ‘Tenure’ as the correct answer. 20% opted for both to be correct while 10% of them were not sure with their attempt.

Advantages of Diagrammatic Presentation

There are several advantages in the presentation of data with the various types of diagrams. They are –

1. Makes it Much Easier to Understand

The presentation of data with the help of diagrams makes it easier for everybody to understand, which thereby makes it easier to grasp the statistics behind the data presented. Diagrammatic data presentation is quite common in newspapers, magazines and even in advertising campaigns so that the common mass can understand what the data is trying to reveal. 

2. Presentation is Much Simpler

With the help of diagrams, presentation of extreme values – extensive unstable data as well as small complicated data complex can be simplified exponentially. 

3. Comparison Operations are More Interactive

Datasets that require comparison of their elements use the application of diagrams for representation. Not only is the presentation attractive, but it is also ideal for showcasing a comparison in statistics.

4. Accepted Universally

Every academic and professional field, let it be Economics, Commerce, Science, Engineering, Statistics, etc. make use of diagrams across the world. Hence, this metric of data presentation is universally accepted.

5. Improves the Representation of Data as a Whole

Statistics are incomplete if diagrams are tables that are not implemented for the presentation of data. Hence, the use of diagrams helps in the overall statistical concept of data representation.

Students who are looking forward to diving deep into the theories and principles of Diagrammatic representation of data, make sure to visit the official website of Vedantu and join a live online tutoring class!

Relevance of Diagrammatic Presentation of Data

Diagrams are visually pleasing and are a great way of representing any form of data. The heavy statistics that we generate can be easily represented via diagrams such as bar charts, pie charts etc. It makes the presentation look neater and more organized. They visually aid the reader in understanding the exact situation and are also very easy to look at.  They save a lot of time and confusion and have a universal utility .  All students must learn how to represent data through diagrams so that they can present facts and figures in an organized manner.

Does Vedantu have Anything on the Diagrammatic Presentation of Data?

Vedantu has ample study material on the diagrammatic representation of data. All students can read from Diagrammatic Presentation of Data and know more. This is available completely free of cost on the platform so that the students do not hesitate before accessing them.

FAQs on Diagrammatic Presentation of Data

1. Which are the types of diagrams used in data representation?

The types of diagrams used in the representation of data are line diagrams, bar diagrams, pie charts and a few others. These are used to represent facts as they make it easier for the students to understand certain information. More about this has been explained in the Diagrammatic Presentation of Data. This page has relevant information that the students can use to understand these diagrams. After having gone through this page, they will know how to represent certain information in the form of diagrams.

2. Are there any merits of the diagrammatic representation of data?

There are a couple of merits of the diagrammatic representation of data. Some of which is that it makes it much easier to understand data, the presentation is simpler, it becomes easier to compare and correlate, and it is universally accepted. 

This page has all the details that are needed by the students to know. It is always better to present data in the form of diagrams as it makes it much more systematic. An organized manner of depicting figures makes anything simpler to understand. 

3. Is a pie chart an accurate way of representing data diagrammatically?

In a pie chart, the sectors of a circle are used as the data points of a particular dataset. It is indeed an accurate method of representing data as the correct percentage can be found out. All students can check out the Diagrammatic Presentation of Data on Vedantu. This page has all the information that’s needed by the participants. The other forms of diagrams that can be utilized for data presentations have also been talked about. This page has been created by expert Commerce teachers who know the topic inside out and can be read by all those who wish to do well in the tests.

4. Difference between the Diagrammatic and Graphical Presentation of Data.

All graphical representations of data can be a diagram, but all diagrams are not a graph. Graphs are represented on a scale, but diagrams are required to be constructed to a scale. Construction of graphs requires two more axes, but none is a necessity in case of diagrams.

5. What are the different Types of Diagrams in Statistics?

The different types of diagrams used in statistics are line diagram, bar diagram, and pie chart. Bar diagrams can further be classified into simple bar diagrams, multiple bar diagrams and component or sub-divided bar diagrams.

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• Diagrammatic Presentation Of Data

Diagrammatic Presentation of Data

The diagrammatic presentation of data gives an immediate understanding of the real situation to be defined by the data in comparison to the tabular presentation of data or textual representations. It translates the highly complex ideas included in numbers into a more concrete and quickly understandable form pretty effectively. Diagrams may be less certain but are much more efficient than tables in displaying the data. There are many kinds of diagrams in general use. Amongst them the significant ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

Also check: Meaning and Objective of Tabulation

Basics of Diagrammatic Presentation

Concept of Diagrammatic Presentation

• It is a technique of presenting numeric data through pictograms, cartograms, bar diagrams, and pie diagrams. It is the most attractive and appealing way to represent statistical data. Diagrams help in visual comparison and they have a bird’s eye view.
• Under pictograms, we use pictures to present data. For example, if we have to show the production of cars, we can draw cars. Suppose the production of cars is 40,000, we can show it by a picture having four cars, where 1 car represents 10,000 units.
• Under cartograms, we make use of maps to show the geographical allocation of certain things.
• Bar diagrams are rectangular and placed on the same base. Their heights represent the magnitude/value of the variable. The width of all the bars and the gaps between the two bars are kept the same.
• Pie diagram is a circle that is subdivided or partitioned to show the proportion of various components of the data.
• Out of the given diagrams, only one-dimensional bar diagrams and pie diagrams are there in our scope.

General Guidelines

Title: Every diagram must be given a suitable title which should be small and self-explanatory.

Size: The size of the diagram should be appropriate, i.e., neither too small nor too big.

Paper used: Diagrams are generally prepared on blank paper.

Scale: Under one-dimensional diagrams, especially bar diagrams, the y-axis is more important from the point of view of the decision of scale because we represent magnitude along this axis.

Index: When two or more variables are presented and different types of line/shading patterns are used to distinguish, an index must be given to show their details.

Selection of proper type of diagram: It is very important to select the correct type of diagram to represent data effectively.

Advantages of Diagrammatic Presentation

(1) Diagrams are attractive and impressive:   The data presented in the form of diagrams can attract the attention of even a common man.

(2) Easy to remember:    (a)  Diagrams have a great memorising effect. (b)  The picture created in mind by the diagrams last much longer than those created by figures presented through the tabular forms.

(3) Diagrams save time : (a)  They present complex mass data in a simplified manner. (b)  The data presented in the form of diagrams can be understood by the user very quickly.

(4) Diagrams simplify data:   Diagrams are used to represent a huge mass of complex data in a simplified and intelligible form which is easy to understand.

(5) Diagrams are useful in making comparison:   It becomes easier to compare two sets of data visually by presenting them through diagrams.

(6) More informative :   Diagrams not only depict the characteristics of data but also bring out other hidden facts and relations which are not possible from the classified and tabulated data.

Types of One-Dimensional Diagram

One-dimensional diagram is a diagram in which only the length of the diagram is considered. It can be drawn in the form of a line or various types of bars.

The following are the types of one-dimensional diagram.

(1) Simple bar diagram

Simple bar diagram consists of a group of rectangular bars of equal width for each class or category of data.

(2) Multiple bar diagram

This diagram is used when we have to make a comparison between two or more variables like income and expenditure, import and export for different years, marks obtained in different subjects in different classes, etc.

(3) Subdivided bar diagram

This diagram is constructed by subdividing the bars in the ratio of various components.

(4) Percentage bar diagram

The subdivided bar diagram presented on a percentage basis is known as the percentage bar diagram.

(5) Broken-scale bar diagram

This diagram is used when the value of one observation is very high as compared to the other.

To gain space for the smaller bars of the series, the larger bars may be broken.

The value of each bar is written at the top of the bar.

(6) Deviation bar diagram

Deviation bars are used to represent net changes in the data like net profit, net loss, net exports, net imports, etc.

Meaning of Pie Diagram

A pie diagram is a circle that is divided into sections. The size of each section indicates the magnitude of each component as a part of the whole.

Steps involved in constructing pie diagram

• Convert the given values into percentage form and multiply it with 3.6’ to get the amount of angle for each item.
• Draw a circle and start the diagram at the 12 O‘clock position.
• Take the highest angle first with the protector (D) and mark the lower angles successively.
• Shade different angles differently to show distinction in each item.

Solved Questions

Q.1. Why is a diagrammatic presentation better than tabulation of data?

It makes the data more attractive as compared to tabulation and helps in visual comparison.

Q.2. Why do media persons prefer diagrammatic presentation of data?

Because it has an eye-catching effect and a long-lasting impact upon its readers/viewers.

Q.3. What will be the degree of an angle in the pie diagram if a family spends 50% of its income in food?

(50 ÷ 100) X 360 (Or) 50 x 3.6 = 180’

Q.4. Which bar diagram is used to show two or more characteristics of the data?

Multiple bar diagram

Q.5. Mention the sum of all the angles formed at the centre of a circle.

Q.6. Name a bar diagram where the height of all the bars is the same.

Percentage bar diagram

Q.7. Which diagram can be used to depict various components of a variable?

Subdivided bar diagram

Q.8. What is a multiple bar diagram?

A multiple bar diagram is one that shows more than one characteristic of data.

Q.9. Which bar diagram is used to represent the net changes in data?

Deviation bar diagram

Q.10. What is the other name of the subdivided bar Diagram?

Component bar diagram

The above-mentioned concept is for CBSE Class 11 Statistics for Economics – Diagrammatic Presentation of Data. For solutions and study materials, visit our website or download the app for more information and the best learning experience.

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Diagrammatic Representation of Geographical Data

• First Online: 30 November 2021

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• Swapan Kumar Maity 3  

Part of the book series: Advances in Geographical and Environmental Sciences ((AGES))

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Diagrammatic representation and visualization of geographical data is very simple, attractive and easy to understand and explain to the geographers as well as to the common literate people. It helps to explore the nature of data, the pattern of their spatial and temporal variations and understanding their relationships to accurately recognize and analyse features on or near the earth’s surface. This chapter focuses on the detailed discussion of various types of diagrams classified on a different basis. All types of one-dimensional (bar, pyramid etc.), two-dimensional (circular, triangular, square etc.), three-dimensional (cube, sphere etc.) and other diagrams (pictograms and kite diagram) have been discussed with suitable examples in terms of their appropriate data structure, necessary numerical (geometrical) calculations, methods of construction, appropriate illustrations, and advantages and disadvantages of their use. It includes all the fundamental geometric principles and derivation of formulae used for the construction of these diagrams. A step-by-step and logical explanation of their construction methods becomes helpful for the readers for an easy and quick understanding of the essence of the diagrams. Each diagram represents a perfect co-relation between the theoretical knowledge of various geographical events and phenomena and their proper practical application with suitable examples.

• Diagrammatic representation
• Geometric principles
• One-dimensional diagram
• Two-dimensional diagram
• Three-dimensional diagram

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Sarkar A (2015) Practical geography: a systematic approach. Orient Blackswan Private Limited, Hyderabad, Telengana, India. ISBN: 978-81-250-5903-5

Sharma PD (1975) Ecology and environment. Rastogi Publications, Gangitri, Shivaji Road, Meerut-250002, ISBN: 978–93–5078–122–7

Singh RL, Singh RPB (1991) Elements of practical geography. Kalyani Publishers, New Delhi

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Maity, S.K. (2021). Diagrammatic Representation of Geographical Data. In: Essential Graphical Techniques in Geography. Advances in Geographical and Environmental Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-16-6585-1_3

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2024 NCAA tournament schedule, scores, highlights

Saturday, March 30 (Elite Eight)

• (1) UConn vs. (3) Illinois | 6:09 p.m. | TBS/truTV
• (4) Alabama vs. (6) Clemson | 8:49 p.m. | TBS/truTV

Sunday, March 31 (Elite Eight)

• (1) Purdue vs. (2) Tennessee | 2:20 p.m. | CBS
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Saturday, April 6 (Final Four)

• TBD vs. TBD

Monday, April 8 (National championship game)

• TBD vs. TBD | 9:20 p.m.

Tuesday, March 19 (First Four in Dayton, Ohio)

• (16) Wagner 71 , (16) Howard 68
• (10) Colorado State 67 , (10) Virginia 42

Wednesday, March 20 (First Four in Dayton, Ohio)

• (16) Grambling 88 , (16) Montana State 81
• (10) Colorado 60 , (10) Boise State 53

Thursday, March 21 (Round of 64)

• (9) Michigan State 66 , (8) Mississippi State 51
• (11) Duquesne 71 , (6) BYU 67
• (3) Creighton 77 , (14) Akron 60
• (2) Arizona 85 , (15) Long Beach State 65
• (1) North Carolina 90 , (16) Wagner 61
• (3) Illinois 85 , (14) Morehead State 69
• (11) Oregon 87 , (6) South Carolina 73
• (7) Dayton 63 , (10) Nevada 60
• (7) Texas 56 , (10) Colorado State 44
• (14) Oakland 80 , (3) Kentucky 76
• (5) Gonzaga 86 , (12) McNeese 65
• (2) Iowa State 82 , (15) South Dakota State 65
• (2) Tennessee 83 ,   (15) Saint Peter's 49
• (7) Washington State 66 , (10) Drake 61
• ( 11) NC State 80 , (6) Texas Tech 67
• (4) Kansas 93 , (13) Samford 89

Friday, March 22 (Round of 64)

• (3) Baylor 92 ,   (14) Colgate 67
• (9) Northwestern 77 , (8) Florida Atlantic 65  (OT)
• (5) San Diego State 69 , (12) UAB 65
• (2) Marquette 87 ,   (15) Western Kentucky 69
• (1) UConn 91 , (16) Stetson 52
• (6) Clemson 77 , (11) New Mexico 56
• (10) Colorado 102 , (7) Florida 100   
• (13) Yale 78 , (4) Auburn 76 
• (9) Texas A&M 98 , (8) Nebraska 83
• (4) Duke 64 , (13) Vermont 47
• (1) Purdue 78 , (16) Grambling 50
• (4) Alabama 109 , (13) College of Charleston 96
• (1) Houston 86 , (16) Longwood 46
• (12) James Madison 72 , (5) Wisconsin 61
• (8) Utah State 88 , (9) TCU 72 
• (12) Grand Canyon 77 , (5) Saint Mary's 66

Saturday, March 23 (Round of 32)

• (2) Arizona 78,  (7) Dayton 68
• (5) Gonzaga 89 , (4) Kansas 68
• (1) North Carolina 85 , (9) Michigan State 69
• (2) Iowa State 67 , (7) Washington State 56
• (11) NC State 79 , (14) Oakland 73
• (2) Tennessee 62 , (7) Texas 58
• (3) Illinois 89 , (11) Duquesne 63 
• (3) Creighton 86 , (11) Oregon 73 (2OT)

Sunday, March 24 (Round of 32)

• (2) Marquette 81,  (10) Colorado 77
• (1) Purdue 106,  (8) Utah State 67
• (4) Duke 93 , (12) James Madison 55 
• (6) Clemson 72 , (3) Baylor 64
• (4) Alabama 72 , (12) Grand Canyon 61
• (1) UConn 75 , (9) Northwestern 58
• (1) Houston 100 , (9) Texas A&M 95 (OT)
• (5) San Diego State 85 , (13) Yale 57 

Thursday, March 28 (Sweet 16)

• (6) Clemson 77 , (2) Arizona 72
• (1) UConn 82 , (5) San Diego State 52
• (4) Alabama 89 , (1) North Carolina 87
• (3) Illinois 72 , (2) Iowa State 69

Friday, March 29 (Sweet 16)

• (11) NC State 66 , (2) Marquette 58
• (1) Purdue 80 , (5) Gonzaga 68
• (4) Duke 54 , (1) Houston 51
• (2) Tennessee 82 , (3) Creighton 75

• CBS Sports and TNT Sports Announce Tip Times and Commentators for Regional Finals on Sunday, March 31

• Latest bracket, schedule and scores for 2024 NCAA men's tournament

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Di men's basketball news.

• This year's Elite Eight teams are all looking to change narratives with a Final Four run
• Tracking 2024 March Madness men's records by conference
• 2024 NIT semifinals and championship sold out
• TNT Sports and CBS Sports Announce Tip Times and Commentators for Regional Finals on Saturday, March 30
• How First Four teams do in the NCAA tournament
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