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  • Find the mean deviation about the median. (3) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

3. Find the mean deviation about the median.

   \small 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Answers (1)

best_answer

Number of observations, n = 12, which is even.

Arranging the values in ascending order:

10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18.

Now, Median (M)

\\ = \frac{(\frac{12}{2})^{th} observation + (\frac{12}{2}+ 1)^{th} observation}{2} \\ = \frac{13 + 14}{2} = \frac{27}{2}= 13.5

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

3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5

\therefore  \sum_{i=1}^{8}|x_i - 13.5| = 28

\therefore M.D.(M) = \frac{1}{12}\sum_{i=1}^{n}|x_i - M|

= \frac{28}{12} = 2.33

Hence, the mean deviation about the median is 2.33.

Posted by

HARSH KANKARIA

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