# Following are the marks obtained by $9$ students in a mathematics test: $50,69,20,33,53,39,40,65,59$ The mean deviation from the median is :

$\begin{array}{1 1}(A)\; 9\\(B)\;10.5\\(C)\;12.67\\(D)\;14.76\end{array}$

Toolbox:
• Median M $= \bigg( \large\frac{N+1}{2} \bigg)$ th observation
• Mean deviation about mean = $\large\frac{\sum|x_i -M|}{n}$
Median M $= \bigg( \large\frac{N+1}{2} \bigg)$ th observation
N=9
$\therefore \bigg(\large\frac{9+1}{2}\bigg)$th observation.
$\qquad= \large\frac{10}{2}$th observation
$\qquad = 5$ th observation
Median (M)=53
$x_i =50; \qquad |x_i-M|=|50-53|=3$
$x_i =69; \qquad |x_i-M|=|69-53|=16$
$x_i =20; \qquad |x_i-M|=|20-53|=33$
$x_i =33; \qquad |x_i-M|=|33-53|=20$
$x_i =53; \qquad |x_i-M|=|53-53|=0$
$x_i =39; \qquad |x_i-M|=|39-53|=14$
$x_i =40; \qquad |x_i-M|=|40-53|=13$
$x_i =65; \qquad |x_i-M|=|65-53|=12$
$x_i =59; \qquad |x_i-M|=|59-53|=6$
$\qquad =117$
Mean deviation about mean = $\large\frac{\sum|x_i -M|}{n}$
$\qquad= \large\frac{117}{9}$
$\qquad= 13$
The nearest option is $12.67$
Hence C is the correct answer.