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

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

JEE MainJEE Main 2022Statistics

Solution:

$ 3,5,7,2 k , 12,16,21,24 $
Median $=\frac{2 k +12}{2}= k +6$
M.D. $=\frac{\Sigma\left| x _{ i }- M \right|}{8}=6 $
$=( k +3)+( k +1)+( k -1)+(6- k )+(6- $
$k )+(10- k )+(15- k )+(18- k )=48$
$ =58-2 k =48 $
$ k =5$
Median $= k +6=11$