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

Answers (1)
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 13^{th} and 14^{th} observations.

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

Therefore, Median, M  = \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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