Question

If the mean deviation of numbers, $1,1+d,1+2d$, $\dots ,1+100d$ from their mean is 255 , then $d$ is equal to

• A. $10.0$
• B. $20.0$
• C. $10.1$
• D. $20.2$

Answer 1

Answer: (D)

$\bar{x}=\frac{\text{ Sum of quantities }}{n}=\frac{\frac{n}{2}(a+l)}{n}$
$=\frac{1}{2}[1+1+100d]=1+50d$
$\therefore MD=\frac{1}{n}\Sigma \left|x_i-\bar{x}\right|$
$\Rightarrow 255=\frac{1}{101}[50d+49d+\dots +d+0+d+\dots +50d]$
$\Rightarrow 255=\frac{2d}{101}\left[\frac{50\times 51}{2}\right]$
$\Rightarrow d=\frac{255\times 101}{50\times 51}=10.1$