$\text { S.D. }=\sqrt{\frac{\sum\left( x _{ i }- x \right)^2}{ n }}$

$\text { M.D. }=\frac{\sum\left| x _{ i }- x \right|}{ n }$

Let $\left| x _{ i }- x \right|= y _{ i }$

$\text { i.e. }\left( x _{ i }- x \right)^2=\left| x _{ i }- x \right|^2= y _{ i }^2$

$\operatorname{Now}(\text { S.D. })^2-(\text { M.D. })^2=\frac{\sum\left( x _{ i }- x \right)^2}{ n }-\left(\frac{\sum\left| x _{ i }- x \right|}{ n }\right)^2$

$=\frac{\Sigma y _1^2}{ n }-\left(\frac{\Sigma y _{ i }}{ n }\right)^2=\sigma_1^2>0\left(\because \sigma^2\right.$ is non negative and all values are not same $)$

$\Rightarrow( S . D .)^2-( M . D .)^2 > 0$

$\Rightarrow S.D > M . D$