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  • If the mean deviation about median for the numbers ,  arranged in the ascen

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

Option: 1

11.5


Option: 2

10.5


Option: 3

12


Option: 4

11


Answers (1)

best_answer

There are 8 (eve) number of terms

\mathrm{\therefore \text { Median }=\frac{2 k+12}{2}=k+6}

Mean deviation about median

\mathrm{\begin{aligned} &6=|k+3|+|k+1|+|k-1|+|k-6|\\ &\frac{+|6-k|+|10-k|+|15-k|+\mid 18-k !}{8} \end{aligned}}

Now acseding order, so

\mathrm{7<2 k<12 \Rightarrow 3.5<k<6}

\mathrm{\Rightarrow \quad 48=5 {8}-2 k} \\

\mathrm{\Rightarrow k=5} \\

\mathrm{\text { Median }=k+6=11}

Hence correct option is 4

 

Posted by

rishi.raj

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