"If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :"

Question

Accepted Answer

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Median $= {{2k + 12} \over 2} = k + 6$

Mean deviation $= \sum {{{|{x_i} - M|} \over n} = 6}$

$$ \Rightarrow {{(k + 3) + (k + 1) + (k - 1) + (6 - k) + (6 - k) + (10 - k) + (15 - k) + (18 - k)} \over 8}$$

$\therefore$ ${{58 - 2k} \over 8} = 6$

$k = 5$

Median $= {{2 \times 5 + 12} \over 2} = 11$

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If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :