In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is 

Solution:

Let $x_i/f_i;i=1,2,\dots ,n$ be a frequency

distribution. Then,

$=\sqrt{\frac{1}{N}\sum _{i=1}^n f_i{\left(x_i-\overline{X}\right)}^2}$ and $\text{ M.D. }=\frac{1}{N}\sum _{i=1}^n f_i\left|x_i-\overline{X}\right|$

let $\left|x_i-\overline{X}\right|=z_i;i=1,2,\dots ,n.$ Then,

${\text{ (S.D.) }}^2-(\text{ M.D. }{)}^2=\frac{1}{N}\sum _{i=1}^n f_i{z}_i^2-{\left(\frac{1}{N}\sum _{i=1}^n f_i{z}_i\right)}^2={\sigma }_z^2\ge 0$

$\Rightarrow \text{ S.D. }>\text{ M.D. }$