Measures of variation are needed for four basic purposes:
Measures of variation point out as to how far an average is representative of the mass. When dispersion is small, the average is a typical value in the sense that it closely represents the individual value and it is reliable in the sense that it is a good estimate of the average in the corresponding universe. On the other hand, when dispersion is large, the average is not so typical, and unless the sample is very large, the average may be quite unreliable.
Another purpose of measuring dispersion is to determine nature and cause of variation in order to control the variation itself. In matters of health variations in body temperature, pulse beat and blood pressure are the basic guides to Prescribed treatment is designed to control their variation.
In industrial production efficient operation requires control of quality variation the causes of which are sought through inspection is basic to the control of causes of variation. In social sciences a special problem requiring the measurement of variability is the measurement of "inequality" of the distribution of income or wealth etc.
Measures of dispersion enable a comparison to be made of two or more series with regard to their The study of variation may also be looked upon as a means of determining uniformity of consistency.
A high degree of variation would mean little uniformity or consistency whereas a low degree of variation would mean great uniformity or consistency.
Many powerful analytical tools in statistics such as correlation analysis. the testing of hypothesis, analysis of variance, the statistical quality control, regression analysis is based on measures of variation of one kind.