Question

If the mean deviation of the numbers $1,1+d,....,1+100d$ from their mean is $255$, then a value of $d$ is:

• A. $10.1$
• B. $20$
• C. $10$
• D. $20.2$

Answer 1

The correct option is A $10.1$

$1,1+d,....,1+100d$ from their mean is $255.$
Mean $=\frac{1+1+d+....+1+100d}{101}$
Mean $=1+50d$
Mean deviation $=\frac{\sum |x-\overline{x}|}{n}$
$255=\frac{(1-(1+50d\left)\right)+\left(\right(1+d)-(1+50d\left)\right)+..\left(\right(1+50d)-(1+50d\left)\right)+..+\left(\right(1+100d)-(1+50d\left)\right)}{101}$
Solving above equation, we get
$255=\frac{2(1d+2d+...50d)}{101}$
Simplifying $d=10.1$