explain diagrammatic presentation of data

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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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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

Diagrammatic Presentation of Data

• First Online: 24 August 2018

Cite this chapter

• Charan Singh Rayat 2  

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The most important function of science of statistics is to simplify the complexity of quantitative data and to make them easily understandable. Numeric figures are usually avoided by common man, but pictures, diagrams, and graphs always attract our attention. Diagrams and graphs give a “birds’ eye view” to the entire mass of statistical data that have been collected about any hypothesis. Characteristics of diagrams and rules for drawing these have been discussed with limitations and use of these. There are a variety of diagrams like dimensional drawings, pictograms, cartograms, graphs, curves, and circles or pie diagrams, which have great utility in the presentation of data.

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Rayat, C.S. (2018). Diagrammatic Presentation of Data. In: Statistical Methods in Medical Research. Springer, Singapore. https://doi.org/10.1007/978-981-13-0827-7_4

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• Diagrammatic Presentation of Data

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.

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.

Presentation of Data

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

What is Meant by Presentation of Data?

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

Presentation of Data Examples

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

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

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

Find the range for the given data.

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

The data given is called the raw data.

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

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

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

Therefore, Range = 95-25 = 70.

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

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

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

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

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

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

Therefore, the presentation of data is given as below:

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

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

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

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

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

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

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

Practice Problems

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

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• Graphic Presentation of Data

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

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Construction of a graph.

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

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

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

Browse more Topics under Descriptive Statistics

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

Some points to remember:

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

General Rules for Graphic Presentation of Data and Information

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

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

Merits of a Graph

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

Limitations of a Graph

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

Types of Graphs

Graphs are of two types:

• Time Series graphs
• Frequency Distribution graphs

Time Series Graphs

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

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

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

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

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

Disadvantages

• It is only used with continuous data.

Use of a false Base Line

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

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

Net Balance Graph

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

Frequency Distribution Graphs

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

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

Frequency Polygon or Histograph

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

Frequency Curve

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

Cumulative Frequency Curve or Ogive

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

Scatter Diagram

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

Solved Question

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

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

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

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Textual Presentation of Data: Meaning, Suitability, and Drawbacks

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

Textual Presentation

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

Suitability

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

Advantages of Textual Presentation of Data

Textual Presentation of Data has the following benefits:

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

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

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

Disadvantages of Textual Presentation of Data

Textual Presentation of Data has the following drawbacks:

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

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

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

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