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.