8.   Find the mean deviation about the median.

   \small x_i            \small 15            \small 21            \small 27            \small 30            \small 35

    \small f_i            \small 3                \small 5             \small 6              \small 7             \small 8

Answers (1)
x_i f_i c.f. |x_i - M| f_i|x_i - M|
15 3 3 13.5 40.5
21 5 8 7.5 37.5
27 6 14 1.5 9
30 7 21 1.5 10.5
35 8 29 6.5 52

Now, N = 30, which is even.

Median is the mean of 15^{th} and 16^{th} observations.

Both these observations lie in the cumulative frequency 21, for which the corresponding observation is 30.

Therefore, Median, M  = \frac{15^{th} observation + 16^{th} observation}{2} = \frac{30 + 30}{2} = 30

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

\sum f_i|x_i - M| = 149.5

\therefore M.D.(M) = \frac{1}{29}\sum_{i=1}^{5}|x_i - M|

= \frac{149.5}{29} = 5.1

Hence, the mean deviation about the median is 5.1

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