Mean Deviation and Coefficient of Mean Deviation

Mean Deviation (M.D.) measures the average of the absolute deviations of every observation from a chosen central value — usually the mean or the median (deviations are taken as absolute values, ignoring sign, because the deviations on either side of the average otherwise sum exactly to zero).

Individual series (n observations $x_i$):

Discrete / continuous series (frequency $f_i$, total frequency $N=\sum f_i$; for a continuous series $x_i$ is the class mid-point):

where $A$ is the average used (mean $\overline{x}$ or median $Md$).

Merits: uses every observation in the data set (unlike Range or Q.D.); less affected by extreme values than the Standard Deviation, since deviations are not squared. …