Q.The marks obtained by 8 students in a class test are: $6, 7, 10, 12, 13, 4, 8, 12$. Find the mean deviation about the mean.

The mean deviation about a central value $a$ (usually the mean $\bar x$ or the median $M$) is the average of the absolute deviations of every observation from $a$: $\text{M.D.}(\bar x)=\dfrac1n\sum|x_i-\bar x|$ and $\text{M.D.}(M)=\dfrac1n\sum|x_i-M|$ for ungrouped data. The absolute value is essential because the plain (signed) deviations from the mean always sum to exactly zero — squaring or taking the absolute value are the two standard ways to prevent this cancellation, and mean deviation uses the absolute value. The mean deviation about the median is always the smallest possible mean deviation for a given data set, among all possible reference points.