Elementary Statstics

7.1.1 DISPERSION

Averages or the measures of central tendency give us an idea 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 well be clear from the following example:

Consider the series (i) 7, 8, 9, 10, 11 (ii) 3, 6, 9, 12, 15 (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 sum is 45. Thus we see that the measures of central tendency are inadequate to give us a complete idea of the distribution. They must be supported and supplemented by some other measures. One such measure is Dispersion.

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).

i) It should be rigidly defined

ii) It should be easy to calculate and easy to understand

iii) It should be based on all the observations

iv) It should be amenable to further mathematical treatment

v) It should be affected as little as possible by fluctuations of sampling