# 7. Find the mean deviation about the median.       $\small x_i$            $\small 5$            $\small 7$            $\small 9$            $\small 10$            $\small 12$            $\small 15$      $\small f_i$             $\small 8$            $\small 6$            $\small 2$              $\small 2$             $\small 2$              $\small 6$

 $x_i$ $f_i$ $c.f.$ $|x_i - M|$ $f_i|x_i - M|$ 5 8 8 2 16 7 6 14 0 0 9 2 16 2 4 10 2 18 3 6 12 2 20 5 10 15 6 26 8 48

Now, N = 26 which is even.

Median is the mean of $\dpi{100} 13^{th}$ and $\dpi{100} 14^{th}$ observations.

Both these observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

Therefore, Median, M  $\dpi{100} = \frac{13^{th} observation + 14^{th} observation}{2} = \frac{7 + 7}{2} = \frac{14 }{2} = 7$

Now, we calculate the absolute values of the deviations from median, $|x_i - M|$  and

$\sum f_i|x_i - M|$ = 84

$\therefore$ $M.D.(M) = \frac{1}{26}\sum_{i=1}^{6}|x_i - M|$

$= \frac{84}{26} = 3.23$

Hence, the mean deviation about the median is 3.23

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