Question

If the mean deviation of numbers, $1,1+d, 1+2 d$, $\ldots, 1+100 d$ 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)

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