DIAGRAMMATIC REPRESENTATION OF DATA

An attractive representation of statistical data is provided by charts, diagrams and pictures.

Diagrammatic representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation.

However, compared to tabulation, this is less accurate.

So if there is a priority for accuracy, we have to recommend tabulation.

We are going to consider the following types of diagrams :

1. Line diagram

2. Histogram

3. Bar diagram

4. Pie chart

Line Diagram

When the time series exhibit a wide range of fluctuations, we may think of logarithmic or ratio chart where "Log y" and not "y" is plotted against "t".

We use Multiple line chart for representing two or more related time series data expressed in the same unit and multiple – axis chart in somewhat similar situations, if the variables are expressed in different units.

Example :

The profits in thousand of dollars of an industrial house for 2002, 2003, 2004, 2005, 2006, 2007 and 2008 are 5, 8, 9, 6, 12, 15 and 24 respectively. Represent these data using a suitable diagram.

Solution :

We can represent the profits for 7 consecutive years by drawing either a line diagram as given below.

Let us consider years on horizontal axis and profits on vertical axis.

For the year 2002, the profit is 5 thousand dollars. It can be written as a point (2002, 5)

In the same manner, we can write the following points for the succeeding years.

(2003, 8), (2004, 9), (2005, 6), (2006, 12), (2007, 15) and (2008, 24)

Now, plotting all these point and joining them using ruler, we can get the line diagram.

Showing line diagram for the profit of an Industrial House during 2002 to 2008.

Histogram

A two dimensional graphical representation of a continuous frequency distribution is called a histogram.

In histogram, the bars are placed continuously side by side with no gap between adjacent bars.

That is, in histogram rectangles are erected on the class intervals of the distribution. The areas of rectangle are proportional to the frequencies.

Example :

Draw a histogram for the following table which represent the marks obtained by 100 students in an examination :

Solution :

The class intervals are all equal with length of 10 marks.

Let us denote these class intervals along the X-axis.

Denote the number of students along the Y-axis, with appropriate scale.

The histogram is given below.

Bar Diagram

There are two types of bar diagrams namely, Horizontal Bar diagram and Vertical bar diagram.

While horizontal bar diagram is used for qualitative data or data varying over space, the vertical bar diagram is associated with quantitative data or time series data.

Bars i.e. rectangles of equal width and usually of varying lengths are drawn either horizontally or vertically.

We consider Multiple or Grouped Bar diagrams to compare related series. Component or sub-divided Bar diagrams are applied for representing data divided into a number of components. Finally, we use Divided Bar charts or Percentage

Bar diagrams for comparing different components of a variable and also the relating of the components to the whole. For this situation, we may also use Pie chart or Pie diagram or circle diagram.

Example :

The total number of runs scored by a few players in one-day match is given.

Solution :

Draw bar graph for the above data.

Pie Chart

In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the value of all the components .Clearly, the total angle of 360° at the center of the circle is divided according to the values of the components .

The central angle of a component is

= [Value of the component / Total value] x 360°

Sometimes, the value of the components are expressed in percentages. In such cases,

The central angle of a component is

= [Percentage value of the component / 100] x 360°

Example :

The number of hours spent by a school student on various activities on a working day, is given below. Construct a pie chart using the angle measurement.