Question

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

• A. $12$
• B. $10.5$
• C. $11.5$
• D. $11$

Answer 1

The correct option is D $11$

Median $=\frac{2k+12}{2}=k+6$
Mean deviation $=\sum \frac{|x_i-M|}{n}=6$

$\Rightarrow \frac{(k+3)+(k+1)+(k-1)+(6-k)+(6-k)+(10-k)+(15-k)+(18-k)}{8}$
$\therefore \frac{58-2k}{8}=6$
$k=5$
Median $=\frac{2\times 5+12}{2}=11$