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

- 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.

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