Question

If the mean deviation of number $1, 1 + d, 1 + 2d, ….. , 1 + 100d$ from their mean is $255$, then the d is equal to

• A. $11.1$
• B. $20.0$
• C. $10.1$
• D. $20.2$

Answer 1

Answer: (C)

$Mean\left(\bar{x}\right)=\frac{sum\, of\, quantities}{n}=\frac{\frac{n}{2}\left(a+l\right)}{n}=\frac{1}{2}\left[1+1+100d\right]=1+50d$
$M.D.=\frac{1}{n}\sum\left|x_{i}-\bar{x}\right| \Rightarrow 255=\frac{1}{101}\left[50d+49d+48d+....+d+0+d+.....+50d\right]=\frac{2d}{101}\left[\frac{50\times51}{2}\right]$
$\Rightarrow d=\frac{255\times101}{50\times51}=10.1$