Elementary Statistics (1+1)

7.1.5 Mean Deviation

If x_i/f_i, I = 1,2, …..n is the frequency distribution, then mean deviation from the average A (usually mean, median or mode) is given by

Mean deviation =

Where represents the modulus or the absolute value of the deviation (x_i – A), when the –ve sign is ignored.

Since mean deviation is based on all the observations, it is a better measure of dispersion than range or quartile deviation. But the step of ignoring the signs of the deviation (x_i-A) creates artificiality and renders it useless for further mathematical treatment.

It may be pointed out here that mean deviation is least when taken from median.