Question

If the mean deviation about the median of the numbers $a,2a,......,50a$ is $50$, then $|a|$ equals

• A. 3
• B. 4
• C. 5
• D. 2

Answer 1

The correct option is B

4

Median is the mean of ${25}^{th}$ and ${26}^{th}$ observation
$\therefore M=\frac{25a+26a}{2}=25.5a$
Mean deviation about median $M.D.\left(M\right)=\frac{\sum |x_i-M|}{N}$
$\Rightarrow 50=\frac{1}{50}[2\times |a|\times (0.5+1.5+2.5+....24.5\left)\right]\Rightarrow 2500=2|a|\times \frac{25}{2}\left(25\right)\Rightarrow |a|=4$