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Diagrammatic Representations: Basics, Types, Examples

Diagrammatic Representations: The use of diagrams to illustrate statistical data is very essential. The greatest way for representing any numerical data obtained in statistics is through diagrammatic representations. “A picture is worth a thousand words,” according to one famous quote. In comparison to tabular or textual representations, the diagrammatic display of data provides an immediate understanding of the true scenario to be defined by the data.

It efficiently converts the exceedingly complex ideas contained in numbers into a more concrete and readily understandable form. Although diagrams are less certain, they are far more efficient in displaying data than tables. There are numerous types of diagrams in common use. Similarly, the diagrammatic representation of data gives a lot of information regarding the numerical data. Let us learn about diagrammatic representations and their types in detail in this article.

Diagrammatic Representation of Data : Meaning

Representation of any numerical data by using diagrams is known as diagrammatic representation. Diagrammatic data representations give a simple and easy understanding of any numerical data collected as compared with the tabular form of the data or textual form of the data.

One of the famous quotes says that “A picture speaks more than words.” Similarly, to represent the statistical data, the essential tool is the diagrams. Diagrammatic data representations translate the highly complex ideas included in the given numerical data into concrete and pretty effectively in a simple, understandable manner.

Diagrammatic representations use geometrical figures as diagrams to improve the representation of the data. Diagrammatic representations are like visual assistance to the readers.

Basics of Diagrammatic Presentations

Diagrammatic representation of data gives a lot of information regarding numerical data. It is a more attractive and easy way of representing any numerical data in statistics. Diagrammatic representations are like visual assistance to the readers. Diagrammatic representations use the geometrical figures as diagrams to improve the data representation, such as cartography, pictographs, Pie charts, bar diagrams, etc.

• In pictographic representation of the data, we use pictures to represent the data. For example: if a company produces \(40,000\) units of cars, then we can show it by only four cars and mentioning each car represents \(10000\) units.
• In the cartograms, we represent the geographical location of certain things, and we use maps.
• Bar graphs are represented by rectangle bars. The height of the bars gives the value or frequency of the variable. All rectangular bars should have equal width.
• In the pie charts, a circle is divided into parts, such that each part shows the proportion of various data.
• In a line representation of data, we use the line to connect the various portions or parts of the plotted data on the graph.

Learn Everything About Pictographs Here

Advantages of Diagrammatic Presentations

The various advantages of the diagrammatic representations are listed below:

• The diagrammatic representations of the data are more attractive and pretty impressive compared with the tabular form of the data or textual form of the data.
• The diagrammatic representations of the data are easy to remember as they use the geometrical figures as the diagrams.
• The diagrammatic representation of data is easy to understand.
• Diagrammatic data representations translate the highly complex ideas included in the given numerical data into concrete and pretty effectively in a simple, understandable manner.
• Diagrammatic representations also help identify hidden facts or relations in the data that are not observed in the tabular form.
• Diagrammatic representations of the data are a handy tool in the comparison of data.

Types of One-Dimensional Diagrams

In one-dimensional diagrammatic representations of the data, we will consider only the length of the diagram. We have different types of one-dimensional diagrams that are listed below:

• Simple bar diagram
• Multiple bar diagrams
• Subdivided bar diagrams
• Percentage bar diagram
• Deviation bar diagram

Types of Diagrammatic Representations

Diagrammatic representations use the geometrical figures as diagrams to improve the data representation, such as cartographs, pictographs, Pie charts, bar diagrams, etc.

1. Line Diagrams

In the linear diagrammatic representations of the data, we will use the line that connects the points or portions of the various data in the graph by taking two variables on horizontal and vertical axes. Example: The below diagram gives the linear representation of the wildlife population of bears, whales, dolphins.

2. Bar Diagrams

In the bar diagrammatic representation of data, the data can be represented by rectangular bars. The height of the bars gives the value or frequency of the variable. All rectangular bars should have equal width. This is one of the best-used tools for the comparison of the data. Example: Birthdays of different students at the school in the different months.

3. Histograms

Histograms are also similar to bar diagrams; they use rectangular bars to represent the data. But all the rectangular bars are kept without any gaps.

4. Pie Diagrams

Pie Diagram is a diagrammatic representation of data by using circles and spheres. In the pie diagrams, a circle is divided into parts, such that each part shows the proportion of various data. Example: The below pie diagram represents the different modes of transport used by the students.

5. Pictographs

The pictographic representation shows the given data graphically by using images or symbols. The symbol or image is used in the pictographic diagrams describes the frequency of the object in the given set of data. Pictographs provided the information of the given data by using symbols or images. Example: The pictograph diagram below shows the mode of transport used by the number of students using the image, and each image represents the value.

Diagrammatic Representation Examples

Q.1. A bus manufacturing company manufactured the following number of buses for the first eight months of the year, which are represented below:

Q.2. The given table represents the marks obtained by \(120\) kids of class IX in a cycle test \(-1\). Draw the more than type ogive  for the given data:

Ans: The linear graph for the given data can be drawn by taking the students’ marks on the horizontal or \(x-\)axis and the number of students on the vertical axis or \(y-\)axis. Then plot the points as finding the marks and number of students in the graph. Now join the points to obtain the graph.

Q.3. Show the below-given data in the pie diagram for the number of fruits eaten by the students in a class:

Ans: Total frequency \(300\).

Draw a circle with a compass with any radius. The pie chart is drawn for the above data shown as follows:

Q.4 . Chinmayi noted all toys she bought for her children and relatives as shown in the below tabular form:

Represent the above data in the diagrammatic representations using the pictographs. Ans: To represent the given data in diagrammatic representation using the pictographs below: First, consider the image or symbol representing the particular object Chinmayi bought. Now, represent the data by using the image or symbol chosen.

Q.5 . The number of children of five different batches of an educational institute is given below. Represent the given data by using the bar graph.

Ans: To represent the above data, consider the values of batches on \(x-\)axis and the number of children on the \(y-\)axis.

The above diagram shows the bar diagram of the given data.

In this article, we have studied the definitions of the diagrammatic representations of the data. We also studied the advantages and basics of diagrammatic representations. This article gives the types of diagrammatic representations used along with the constructions. This article studied the solved examples that help us to understand and the construction of diagrammatic representations easily.

FAQs on Diagrammatic and Graphical Representation of Data

The answers to the most frequently asked questions on Diagrammatic and Graphical Representation of Data are provided here:

Q.1. What is a diagrammatic representation of data? Ans: Representation of any numerical data by using diagrams is known as diagrammatic representation.

Q.2. What are the advantages of diagrammatic representations? Ans: Some of the advantages of the diagrammatic representations are listed below: 1. These are more attractive and pretty impressive. 2. These are easy to remember. 3. These are easy to construct and easy to understand. 4. This gives the complex data in the simplest form. 5. These give more information.

Q.3. What is the diagrammatic representation of the problem-solving process? Ans: The diagrammatic representation of problem-solving are: 1. Pictographs 2. Pie charts 3. Bar graphs 4. Histograms 5. Linear diagrams

Q.4. Why is the diagrammatic representation of the data better than the tabulation of the data? Ans: Diagrammatic data representations give a simple and easy understanding of any numerical data collected compared with the tabular form of the data or textual form of the data.

Q.5. What is a one-dimensional diagrammatic representation of data? Ans: The one-dimensional diagrammatic representation of data is: 1. Line diagrams 2. Bar diagrams

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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

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Diagrammatic and Graphic Presentation of Data

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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Diagrammatic Representation and Reasoning

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Diagrammatic Reasoning

Introduction to Diagrams, Visual Models, and Abduction

• artificial intelligence
• cognitive science
• description logic
• human-computer interaction (HCI)
• information system
• intelligence
• linear optimization
• problem solving
• visualization

Table of contents (32 chapters)

Front matter, views of diagrams, diagrams in the mind.

• Aaron Sloman

Knowing About Diagrams

• Robert K. Lindsay

A Meta-Taxonomy for Diagram Research

• Alan Blackwell, Yuri Engelhardt

Sketches as Mental Reifications of Theoretical Scientific Treatment

• Daniela M. Bailer-Jones

The Fundamental Design Variables of Diagramming

• Clive Richards

Cognitive Aspects of Diagrams

Psychological perspectives on diagrams and their users.

• Alan F. Blackwell

Combining Semantic and Cognitive Accounts of Diagrams

• Corin A. Gurr

Tactile Maps and a Test of the Conjoint Retention Hypothesis

• Simon Ungar, Mark Blades, Christopher Spencer

Spatial Abilities in Problem Solving in Kinematics

• Maria Kozhevnikov, Mary Hegarty, Richard Mayer

Graph Comprehension: The Role of Format, Content and Individual Differences

Graphs in print.

• Jeff Zacks, Ellen Levy, Barbara Tversky, Diane Schiano

The Role of Representation and Working Memory in Diagrammatic Reasoning and Decision Making

• Jozsef A. Toth, C. Michael Lewis

Mechanical Reasoning about Gear-and-belt Diagrams: Do Eye-movements Predict Performance?

• Leon Rozenblit, Michael Spivey, Julie Wojslawowicz

How do Designers Shift their Focus of Attention in their Own Sketches?

• Masaki Suwa, Barbara Tversky

Formal Aspects of Diagrammatic Reasoning

Diagrammatic evaluation of visual mathematical notations.

Bernd Meyer

A Topological Framework for Modelling Diagrammatic Reasoning Tasks

• Jean-Louis Giavitto, Erika Valencia

Editors and Affiliations

Michael Anderson

Patrick Olivier

Bibliographic Information

Book Title : Diagrammatic Representation and Reasoning

Editors : Michael Anderson, Bernd Meyer, Patrick Olivier

DOI : https://doi.org/10.1007/978-1-4471-0109-3

Publisher : Springer London

eBook Packages : Springer Book Archive

Copyright Information : Springer-Verlag London Limited 2002

Softcover ISBN : 978-1-85233-242-6 Published: 05 October 2001

eBook ISBN : 978-1-4471-0109-3 Published: 27 June 2011

Edition Number : 1

Number of Pages : XVI, 584

Number of Illustrations : 64 b/w illustrations

Topics : Applications of Mathematics , Artificial Intelligence , Logic

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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 –

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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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Advantages and Disadvantages of Diagrammatic Representation

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We have collected some solid points that will help you understand the pros and cons of Diagrammatic Representation in detail.

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What is Diagrammatic Representation?

What are the advantages and disadvantages of diagrammatic representation.

The following are the advantages and disadvantages of Diagrammatic Representation:

Advantages of Diagrammatic Representation

Disadvantages of diagrammatic representation.

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• Diagrammatic Representation of Data

Suppose you are interested to compare the marks of your mates in a test. How can you make the comparison interesting? It can be done by the diagrammatic representations of data. You can use a bar diagram, histograms, pie-charts etc for this.  You will be able to answer questions like –

How will you find out the number of students in the various categories of marks in a certain test? What can you say about the marks obtained by the maximum students? Also, how can you compare the marks of your classmates in five other tests? Is it possible for you to remember the marks of each and every student in all subjects? No! Also, you don’t have the time to compare the marks of every student. Merely noting down the marks and doing comparisons is not interesting at all. Let us study them in detail.

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Bar diagram.

This is one of the simplest techniques to do the comparison for a given set of data. A bar graph is a graphical representation of the data in the form of rectangular bars or columns of equal width. It is the simplest one and easily understandable among the graphs by a group of people.

Browse more Topics under Statistical Description Of Data

• Introduction to Statistics
• Textual and Tabular Representation of Data
• Frequency Distribution
• Frequency Polygon  
• Cumulative Frequency Graph or Ogive

Construction of a Bar Diagram

• Draw two perpendicular lines intersecting each other at a point O. The vertical line is the y-axis and the horizontal is the x-axis.
• Choose a suitable scale to determine the height of each bar.
• On the horizontal line, draw the bars at equal distance with corresponding heights.
• The space between the bars should be equal.

Properties of a Bar Diagram

• Each bar or column in a bar graph is of equal width.
• All bars have a common base.
• The height of the bar corresponds to the value of the data.
• The distance between each bar is the same.

Types of Bar Diagram

A bar graph can be either vertical or horizontal depending upon the choice of the axis as the base. The horizontal bar diagram is used for qualitative data. The vertical bar diagram is used for the quantitative data or time series data. Let us take an example of a bar graph showing the comparison of marks of a student in all subjects out of 100 marks for two tests.

With the bar graph, we can also compare the marks of students in each subject other than the marks of one student in every subject. Also, we can draw the bar graph for every student in all subjects.

We can use another way of diagrammatical representation of data. If we are working with a continuous data set or grouped dataset, we can use a histogram for the representation of data.

• A histogram is similar to a bar graph except for the fact that there is no gap between the rectangular bars. The rectangular bars show the area proportional to the frequency of a variable and the width of the bars represents the class width or class interval.
• Frequency means the number of times a variable is occurring or is present. It is an area graph. The heights of the rectangles are proportional to the corresponding frequencies of similar classes.

Construction of Histogram

• Choose a suitable scale for both the axes to determine the height and width of each bar
• On the horizontal line, draw the bars with corresponding heights
• There should be no gap between two consecutive bars showing the continuity of the data
• If the grouped frequencies are not continuous, the first thing to do is to make them continuous

It is done by adding the average of the difference between the lower limit of the class interval and the upper limit of the preceding class width to the upper limits of all the classes. The same quantity is subtracted from the lower limits of the classes.

Properties of Histogram

• Each bar or column in a bar graph is of equal width and corresponds to the equal class interval
• If the classes are of unequal width then the height of the bars will be proportional to the ration of the frequencies to the width of the classes
• All bars have a common base
• The height of the bar corresponds to the frequency of the data

Suppose we have a data set showing the marks obtained out of 100 by a group of 35 students in statistics. We can find the number of students in the various marks category with the help of the histogram.

A line graph is a type of chart or graph which shows information when a series of data is joined by a line. It shows the changes in the data over a period of time. In a simple line graph, we plot each pair of values of (x, y). Here, the x-axis denotes the various time point (t), and the y-axis denotes the observation based on the time.

Properties of a Line Graph

• It consists of Vertical and Horizontal scales. These scales may or may not be uniform.
• Data point corresponds to the change over a period of time.
• The line joining these data points shows the trend of change.

Below is the line graph showing the number of buses passing through a particular street over a period of time:

Solved Examples for diagrammatic Representation of Data

Problem 1: Draw the histogram for the given data.

Solution: This grouped frequency distribution is not continuous. We need to convert it into a continuous distribution with exclusive type classes. This is done by averaging the difference of the lower limit of one class and the upper limit of the preceding class. Here, d = ½ (19 – 18) = ½ = 0.5. We add 0.5 to all the upper limits and we subtract 0.5 from all the lower limits.

The corresponding histogram is

Draw a line graph for the production of two types of crops for the given years.

Solution: The required graph is

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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.

• Math Article

Graphical Representation

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

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

General Rules for Graphical Representation of Data

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

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

Graphical Representation in Maths

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

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

Principles of Graphical Representation

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

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

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

Merits of Using Graphs

Some of the merits of using graphs are as follows:

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

Example for Frequency polygonGraph

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

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

Draw the frequency polygon for the following data

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

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

Now calculate the midpoint of the class interval.

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

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

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

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

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

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

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

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Diagrammatic representation of data

What is data interpretation? There are many types of data interpretation. These are such as the diagrammatic and graphical representation of data.

Data interpretation is one of the most important elements of statistical analysis. It is also one of the hardest to master and can be frustrating for students who have not had much experience in statistics.

This interpretation also requires a lot of practice and patience to become proficient at it. As with any other subject, the more you learn statistics, the better your data interpretation skills will be.

Data can be interpreted in two different methods that are a diagrammatic and graphical representation of data.

Data Interpretation

Data is always taken into consideration when interpreting results from a statistical test or experiment. This means that if there are no significant differences between groups then there was likely a bias on either side of the scale (or both sides).

 However, what does this mean exactly? Well let us take an example where we have two groups A and B who were given different treatments but both groups had similar outcomes – they got sick! This could mean one thing: Group A didn’t get sick because of the treatment they received, while Group B did. This would be an example of a Type I error (also called a false positive).

On the other hand, if group A had worse outcomes than group B, this could mean that the treatment had no effect on either group, or it could mean that group A was more susceptible to the treatment. In this case, we would have a Type II error (false negative).

Diagrammatic Representation of Data

The diagrammatic representation of data is a method used in the analysis and exploration of information with the help of diagrams. It refers to different methods that convert numbers into graphic forms, such as bar graphs, circle charts, and histograms.

This also includes the use of color, layout, and shape to encode data. The aim is to make complex information more accessible and easy to understand for everyone.

One common way of representing data is through pie charts. A pie chart is a circular graph divided into sectors, which represent percentages or proportions of a whole. It is used to compare different parts of a whole or track changes over time.

The advantage of using a diagrammatic representation of data is that it can help us see relationships and patterns that may be hidden in numbers alone. They can also help us communicate our findings effectively to others.

Graphical Representation of Data

The graphical representation of data is an important part of scientific communication. It allows scientists to visualize their data and see relationships between different variables.

There are many different types of graphical representations of data, including histograms, scatter plots, and line graphs. Each type of graph has its strengths and weaknesses.

Histograms are good for showing the distribution of a variable, scatter plots are good for showing correlations between two variables, and line graphs are good for showing trends over time.

It is important to choose the right type of graph for your data so that you can communicate your findings accurately and effectively. This also helps to prevent misunderstandings and misinterpretations.

When creating a graphical representation of data, it is important to:

• use the right type of graph for your data
• label all axes correctly
• use appropriate units of measurement
• conclude accurately from the data presented in the graph
• avoid misleading your reader with the data you present

Difference Between Diagrammatic And Graphical Representation of Data

The difference between the diagrammatic and graphical representation of data is that the diagrammatic representation of data shows how much each value deviates from the mean, while the graphical representation shows how the data are distributed. The diagrammatic representation of data is useful for identifying outliers, while the graphical representation is useful for identifying patterns in the data.

The diagrammatic representation of data can be created by calculating the deviation of each datum from the mean and then dividing by the standard deviation. This produces a series of numbers called a “boxplot.” A box plot shows how much each value deviates from the median, as well as how concentrated or dispersed the data are.

The graphical representation of data can be created by plotting points on a graph and then drawing a line or curve through the points. This produces a “graph.” A graph shows how the data are distributed and can be used to identify patterns in the data.

Data representation is a vital aspect of today’s society. Diagrammatic and graphical representation of data is different from a normal presentation that you see in textbooks. This presentation of data enables the viewer to know the exact picture of the situation. It will also help them define various aspects of a problem without just listing down numbers.

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Definition of diagram

 (Entry 1 of 2)

Definition of diagram  (Entry 2 of 2)

transitive verb

• illustration

Examples of diagram in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'diagram.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Greek diagramma , from diagraphein to mark out by lines, from dia- + graphein to write — more at carve

1619, in the meaning defined at sense 1

1785, in the meaning defined above

Phrases Containing diagram

• Argand diagram
• block diagram
• flow diagram
• scatter diagram
• Venn diagram

Dictionary Entries Near diagram

diagram factor

Cite this Entry

“Diagram.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/diagram. Accessed 14 Aug. 2024.

Kids Definition

Kids definition of diagram.

Kids Definition of diagram  (Entry 2 of 2)

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Nglish: Translation of diagram for Spanish Speakers

Britannica English: Translation of diagram for Arabic Speakers

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Meaning of diagrammatic in English

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• A diagrammatic area layout is prepared , showing the ideal space requirement .
• These photographs are almost diagrammatic.
• Diagrammatic drawings provide clear factual information about piano mechanisms .
• block graph
• graph paper
• normal distribution
• scatter diagram
• vertical axis

Examples of diagrammatic

Translations of diagrammatic.

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to press the button on the left of a computer mouse in order to make the computer do something

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Definition of diagrammatic adjective from the Oxford Advanced Learner's Dictionary

diagrammatic

• representation

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