INCOME TAX NOTES

Presentation of Data-Geometric Diagram

Presentation of Data- Geometric Diagram

Presentation of Data-Geometric Diagram

 DIAGRAMMATIC PRESENTATION OF DATA

This is the third method of presenting data. This method provides the quickest understanding of the actual situation to be explained by data in comparison to tabular or textual presentations.
Diagrammatic presentation of data translates quite effectively the highly abstract ideas contained in numbers into more concrete and easily comprehensible form. Diagrams may be less accurate but are much more effective than tables in presenting the data. There are various kinds of diagrams in common use. Amongst them the important ones are the following:
 (i) Geometric diagram
 (ii) Frequency diagram
 (iii) Arithmetic line graph

Geometric Diagram:-
 Bar diagram and pie diagram come in the category of geometric diagram. The bar diagrams are of three types — simple, multiple and component bar diagrams.

a)Bar Diagram
Simple Bar Diagram Bar diagram comprises a group of equi spaced and equi width rectangular bars for each class or category of data. Height or length of the bar reads the magnitude of data




b)Multiple Bar Diagram
 Multiple bar diagrams  are used for comparing two or more sets of data, for example income and expenditure or import and export for different years, marks obtained in different subjects in different classes, etc.



 c)Component Bar Diagram 
Component bar diagrams or charts (Fig.4.3), also called sub-diagrams, are very useful in comparing the sizes of different component parts (the elements or parts which a thing is made up of) and also for throwing light on the relationship among these integral parts.



d)Pie Diagram 
A pie diagram is also a component diagram, but unlike a bar diagram, here it is a circle whose area is proportionally divided among the components (Fig.4.4) it represents. It is also called a pie chart. The circle is divided into as many parts as there are components by drawing straight lines from the center to the circumference. Pie charts usually are not drawn with absolute values of a category.

 Pie charts usually are not drawn with absolute values of a category. The values of each category are first expressed as percentage of the total value of all the categories. A circle in a pie chart, irrespective of its value of radius, is thought of having 100 equal parts of 3.6° (360°/100) each. To find out the angle, the component shall subtend at the center of the circle, each percentage figure of every component is multiplied by 3.6°. An example of this conversion of percentages of components into angular components of the circle is shown below.



Frequency Diagram
 Data in the form of grouped frequency distributions are generally represented by frequency diagrams like histogram, frequency polygon, frequency curve and ogive.

 Histogram 
A histogram is a two dimensional diagram. It is a set of rectangles with base as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency . If the class intervals are of equal width, which they generally are, the area of the rectangles are proportional to their respective frequencies. However, in some type of data, it is convenient, at times necessary, to use varying width of class intervals.

When bases vary in their width, the heights of rectangles are to be adjusted to yield comparable measurements. The answer in such a situation is frequency density (class frequency divided by width of the class interval) instead of absolute frequency.




Frequency Polygon
 A frequency polygon is a plane bounded by straight lines, usually four or more lines. Frequency polygon is an alternative to histogram and is also derived from histogram itself.
Statistics deals with the collection of data and information for a particular purpose. The tabulation of each run for each ball in cricket gives the statistics of the game. Tables, graphs, pie-charts, bar graphs, histograms, polygons etc .are used to represent statistical data pictorially.
Frequency polygon can be fitted to a histogram for studying the shape of the curve. The simplest method of drawing a frequency polygon is to join the midpoints of the topside of the consecutive rectangles of the histogram. A frequency polygon is almost identical to a histogram, which is used to compare sets of data or to display a cumulative frequency distribution. It uses a line graph to represent quantitative data.​




Ogive
 Ogive is also called cumulative frequency curve. As there are two types of cumulative frequencies, for example ‘‘less than’’ type and ‘‘more than’’ type, accordingly there are two ogives for any grouped frequency distribution data. Here in place of simple frequencies as in the case of frequency polygon, cumulative frequencies are plotted along y-axis against class limits of the frequency distribution.
For ‘‘less than’’ ogive the cumulative frequencies are plotted against the respective upper limits of the class intervals whereas for more than ogives the cumulative frequencies are plotted against the respective lower limits of the class interval. An interesting feature of the two ogives together is that their intersection point gives the median. As the shapes of the two ogives suggest, ‘‘less than’’ ogive is never decreasing and ‘‘more than’’ ogive is never increasing.




Arithmetic Line Graph
 An arithmetic line graph is also called time series graph. In this graph, time (hour, day/date, week, month, year, etc.) is plotted along x-axis and the value of the variable (time series data) along y-axis.
 A line graph by joining these plotted points, Frequency distribution of marks obtained in mathematics thus, obtained is called arithmetic line graph (time series graph). It helps in understanding the trend, periodicity, etc., in a long term time series data.

Example: