Standard Deviation

The main drawback of the deviation measures of dispersion, as discussed earlier, is that the positive and negative deviations cancel out each other. Use of the mean absolute deviation overcomes this problem, but creates another. It is difficult to deal with a quantity like   algebraically.The standard deviation is an improved measure of dispersion. Calculation of the standard deviation involves the following four steps:

1. Calculation of deviations of the observations from the mean.

2. Squaring each deviation.

3. Finding the mean of the squared deviations obtained in step (2).

4. Taking the positive square root of the mean found in step (3).

   The standard deviation is denoted by 'σ'

   so,

   σ

   =

   where,

            X   denotes each observation

            μ          is the arithmetic mean of the population

            N   is the number of observations