Measures of dispersion (variations) are calculated to serve the following purposes:
1) Measuring variability determines the reliability of an average by pointing out to what extent the average is representative of the entire data. In Illustration 1 discussed earlier, mean sales Rs. 60,000 is the perfect representative of sales for different days tor Firm A. In case of Firm B , the variation is low as the mean sale is quite close to sales figures of different days. Therefore, in this case, the mean can be considered as representative of the sales for each day. But in case of Firm C the variation in individual figures is very large so the average of Rs. 60,000 is hardly a representative of all high and low figures such as Rs. 2,10,000 and Rs. 18,000.
2) Measures of dispersion enable comparisons of two or more distributions with regard to their variability.
3) Another purpose of measuring variability is to determine the nature and cause of variation in order to control the variation itself.
4) Measuring variability facilitates the use of other statistical measures like correlation, regression, statistical inference, etc.
