Objectives of Measuring Dispersion
a.To judge the Reliability of Measures of Central Tendency: Measure of dispersion is the only means to test the representative character of an average. If the extent of the scatter is less it indicates a greater degree of uniformity in the value of items and as such the average may be regarded as representative. On the other hand if the scatter is large is average is bound to be less reliable since it shows a lower degree of uniformity in the value of observations. It is observed that when dispersion small the average is a typical value which it closely represents the individual values.
b.To Compare Two or More Series with Regard to Their variability : When two series are to be compared due consideration has to be given to their dispersion i e, the extent to which the items are spread around their respective averages. Using measures of dispersion one can find out degree of uniformity or consistency in two or more set of data. For example if it is desired to make a comparison between the price of equity shares of two or more companies over a period of time a measure of dispersion for each such series of prices would be very helpful.
c.To Control the Variability Itself: Measures of dispersion are indispensable in analyzing the nature and locating the causes of variation. According to spur and Bonini in matters of health variation in body temperature pulse beat and blood pressures are basic guides to diagnosis. 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 and quality control programme. In social sciences the measurement of inequality in the distribution of income and wealth requires the measures of variation.
d.To Facilitate the Use of Other Statistical Measure : Many other important statistical techniques like correlation regression test of hypothesis analysis of fluctuations in a time series have roots in the measures of variation of one kind or the other.