Question

Mean square deviation of a distribution is least when deviations are taken about

• A. mean
• B. median
• C. mode
• D. none of these

Answer 1

The correct option is A mean

if $S$ denote the root mean square deviation from same number a, i.e.,
$S=\frac{1}{N}\sum _{i=1}^n{f}_i{(x_i-a)}^2$ and $\sigma$ is the $S.D.$
then $S^2={\sigma }^2+d^2$ where $d=\overline{X}-a$
Clearly, $S$ is least when $d=0\overline{x}=a$
Thus, root mean square deviation is least when deviation are taken from $\overline{x}$