Question

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

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

Answer 1

The correct option is C $10.1$

.: $\frac{\sum |x-\overline{x}|}{n}=255$
$\overline{x}=\frac{1+1+d+1+2d\dots +1+100d}{101}$
$=\frac{101+d\left(\frac{100\times 101}{2}\right)}{101}$
$=1+\frac{50\times 101d}{101}=1+50d$
$\sum {|}_{X-\overline{X}}|=255\times 101$
$2d\left(\frac{50\times 51}{2}\right)=255\times 101$
$d=\frac{255\times 101}{50\times 51}=10.1$