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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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