The standard devidtion, like any other devices has certain merits and demerits. These are outlined here as under:
- It is rigidly defined and free from any ambiguity.
- Its calculation is based on all the observations of a series and it cannot be correctly calculated ignoring any item of a series.
- It strictly follows the algebraic principles, and it never ignores the + and – signs like the mean deviation.
- It is capable of further algebraic treatment as it has a lot of algebraic properties.
- It is used as a formidable instrument in making higher statistical analysis viz.: correlation, skewness, regression and sample studies, etc.
- It is not much affected by the fluctuations in sampling for which is widely used in testing the hypotheses and for conducting the different tests of significance viz. : test, t2 test etc.
- In a normal distribution, X¯ ± 1 covers 68.27% of the values for which it is called a standard measure of dispersion.
- It exhibits the scatter of dispersion of the various items of a series form its arithmetic mean and thereby justifies its name as a measure of dispersion.
- It enables us to make a comparative study of the two, or moiré series, and to tell upon their consistency, or stability through calculation of the important factors viz. co-efficient of variation, variance etc.
- It enables us to determine the reliability of the Mean of the two or more series when they show the identical means.
- It can be calculated through a good number of methods yielding the same results.
- It maintains an empirical relation with other measures of dispersion as under :
Range = 6, QD =2/3 , and MD = 4/5
- It has a good number of algebraic properties for which it is possible to determine the number of many connected factors like combined standard deviation of two or more series.
- It is not understood by a common man.
- Its calculation is difficult as it involves many mathematical models and processes.
- It is affected very much by the extreme values of a series in as much as the squares of deviations of big items proportionately bigger than the squares of the smaller items.
- It cannot be used for comparing the dispersion of two, or more series given in different units.