A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment

A measure of dispersion : A good supplement to the central value : A central value condenses the series into a single figure. The measure of central tendencies indicate the central tendency of a frequency distribution in the form of an average. These averages tell us something about the general level of the magnitude of the distribution, but they fail to show anything further about the distribution. The averages represent the series as a whole. One may now be keen to know how far the various values of the series tend to dispense from each other or from their averages. This brings us to yet another important brand of statistical methods, viz. measures of dispersion. Only when we study dispersion alongwith average of series that we can have a comprehensive information about the nature and composition of a statistical series.

In a country, the average income or wealth may be equal. Yet there may be great disparity in its distribution. As a result, thereof, a majority of people may be below poverty line. There is need to measure variation in dispersion and express it as a single figure. It can be further explained with an example. Below are given the family’s incomes of Ram, Rahim and Maria. Ram, Rahim and Maria have four, six and five members in their families respectively.

Family Income

From the table we come to know that each family have average income of Rs. 15,000

considerable differences in individual methods. It is quite obvious that averages try to tell only one aspect of a distribution i.e. representative size of the values. To understand it better, we need to know the spread of values also. The Ram’s family, differences in incomes are comparatively lower. In Rahim’s family, differences are higher and Maria’s family differences are the highest. Knowledge of only average is sufficient. A measure of dispersion improves the understanding of the distribution series.