Merits:
Among all the measures of dispersion, standard deviation is considered superior because it possesses almost all the requisites of a good measure of dispersion. Standard deviation had the following merits :
i) It is rigidly defined and is based on all observations of the series.
ii) The unique property which makes standard deviation superior to other measures of dispersion is that it is amenable to algebraic treatment. Thus, if we are given the number of observations, mean and standard deviation for each of several groups, we can easily calculate the standard deviation of the composite group.
iii) Standard deviation is least affected by the fluctuations of sampling.
iv) In a normal distribution the mean ± S.D . covers 68.36%,of the values whereas only 50% values are covered by quartile deviation and 57% by mean deviation. Because of this reason, standard deviation is called a ‘standard measure’ .
Limitations :
The main limitations or demerits of standard deviation as a measure of dispersion are as follows:
i) The major limitation of SD is that it cannot be used for comparing the dispersion of two o r more series of observations given in different units. A coefficient of standard deviation has to be defined for this purpose.
ii) The process of squaring deviations from mean and then taking the square-root of the mean of these squared deviations seems to be a complicated affair. In fact this gives rise to another limitation i.e., standard deviation is very much affected by the extreme values. The process of squaring deviations give undue importance to large deviations from arithmetic mean which are obtained only from extreme items and it gives less importance to items which are nearer to mean.
iii) The standard deviation cannot be computed for a distribution with open-and classes.
