Question

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

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

Answer 1

The correct option is B

10.1

$\text{Mean}=\frac{101+d(1+2+3+\cdots +100)}{101}=1+\frac{d\times 100\times 101}{101\times 2}=1+50d$
$\because$ Mean deviation from the mean = 255
$\Rightarrow \frac{1}{101}[|1-(1+50d)|+|(1+d)-(1+50d)|+|(1+2d)-(1+50d)|+\cdots +|(1+100d)-(1+50d\left)|\right]=255\Rightarrow 2d[1+2+3+\cdots +50]=101\times 255\Rightarrow 2d\times \frac{50\times 51}{2}=101\times 255\Rightarrow d=\frac{101\times 255}{50\times 51}=10.1$