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  • Find the mean deviation about the median. (4) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

4.  Find the mean deviation about the median.

    \small 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Answers (1)

best_answer

Number of observations, n = 10, which is even.

Arranging the values in ascending order:

36, 42, 45, 46, 46, 49, 51, 53, 60, 72

Now, Median (M)

\\ = \frac{(\frac{10}{2})^{th} observation + (\frac{10}{2}+ 1)^{th} observation}{2} \\ = \frac{46 + 49}{2} = \frac{95}{2}= 47.5

The respective absolute values of the deviations from median, |x_i - M| are

11.5, 5.5, 2.5, 1.5, 1.5, 1.5, 3.5, 5.5, 12.5, 24.5

\therefore  \sum_{i=1}^{8}|x_i - 47.5| = 70

\therefore M.D.(M) = \frac{1}{10}\sum_{i=1}^{n}|x_i - M|

= \frac{70}{10} = 7

Hence, the mean deviation about the median is 7.

Posted by

HARSH KANKARIA

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