Measures of dispersion

Measures of dispersion

Average gives us an idea on the point of the concentration of the observations about the central part of the distribution. If we know the average alone we cannot form a complete idea about the distribution as will be clear from the following example.

Consider the series (i) 7,8,9,10,11 (ii) 3,6,9,12,15 and (iii) 1,5,9,13,17. In all these cases we see that n, the number of observations is 5 and the mean is 9. If we are given that the mean of 5 observations is 9, we cannot form an idea as to whether it is the average of first series or second series or third series or of any other series of 5 observations whose sum is 45. Thus we see that the measures of central tendency are inadequate to give us a complete idea of the distribution. So they must be supported and supplemented by some other measures. One such measure is Dispersion, which provides the nature of spreadness of the data.

Literal meaning of dispersion is “scatteredness” we study dispersion to have an idea about the homogeneity or heterogeneity of the distribution. In the above case we say that series (i) is more homogeneous (less dispersed) than the series (ii) or (iii) or we say that series (iii) is more heterogeneous (more scattered) than the series (i) or (ii).

Various measures of dispersion can be classified into two broad categories.

(a) The measures which express the spread of observations in terms of distance between the values of selected observations. These are also termed as distance measures.

Example: Range and interquartile range (or) quartile deviation.

(b) The measures which express the spread of observations in terms of the average of deviations of observation from some central value,

Example: Mean deviation and Standard deviation.