Question

If the mean deviation about the median of the numbers $a,2a,\dots$ , $50a$ is $50$, then $|a|$ is equal

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

Median is the mean of 25th and 26th observation
$\therefore M=\frac{25a+26a}{2}=25.5a$
$M.D.(M)=\frac{\Sigma |x_i-M|}{N}$
$50=\frac{1}{50}[2\times |a|\times (0.5+1.5+2.5+\dots 24.5\left)\right]$

$\Rightarrow 2500=2|a|\times \frac{25}{2}\left(25\right)$
$\Rightarrow |a|=4$ .