What is Standard Deviation? How does it differ from Mean Deviation? What are its advantages and disadvantages?

Standard Deviation : Karl Pearson introduced the concept of Standard Deviation in 1893. It is the most popular measure of dispersion since it does not suffer from the defects and limitations which other measures of deviation have. It can be defined as the square root of the mean of the squared deviations taken from the arithmetic mean. It is also called the root mean square deviation. Greek letter ‘s’ (read as sigma) is used to denote the standard deviation.

Features of Standard Deviation. Some features regarding standard deviation should be noted. They are : (i) Greater the amount of standard deviation, greater shall be dispersion or variability. In other words, smaller standard deviation means more homogeneity of data and vice-versa. (ii) If two distributions have the same mean, the one with the smaller standard deviation has a more representative mean.

Advantages of Standard Deviation :

(1) Based on all values : The calculation of Standard Deviation is based on all the values of a series. It does not ignore any value.

(2) Certain Measure : Standard Deviation is a clear and certain measure of dispersion. Therefore, it can be used in all situations.

(3) Little Effect of Sampling : Change in sampling causes little effect on Standard Deviation. This is because deviation is based on all the values of a sample.

(4) Algebraic Treatment : Standard Deviation is capable of further algebraic treatment.

Disadvantages of Standard Deviation :

(1) Difficult : Standard Deviation is difficult to calculate or understand.

(2) More importance to Extreme Value : In the calculation of standard deviation extreme values get greater importance.

Distinction between Mean Deviation and Standard Deviation :

Both of them are based on all the items of a distribution, but they are different from each -other in the following ways :

(i) In calculating the mean deviation algebraic signs are ignored. But they are considered in calculating the standard deviation.

(ii) Median or mean is used in calculating the mean deviation. But only mean is used to calculate the standard deviation.