Question

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

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

Answer 1

The correct option is C $10.1$

Mean, $\overline{x}=\frac{\frac{101}{2}(1+1+100d)}{101}=1+50d$
Mean deviation $=\frac{1}{n}\sum |x_i-\overline{x}|$
$\Rightarrow 255=\frac{1}{101}(50d+49d+\cdots +d+0+d+\cdots +50d)$
$\Rightarrow 255=\frac{2d}{101}\left(\frac{50\times 51}{2}\right)$
$\Rightarrow d=10.1$