Question

If the mean deviation of number $1,1+d,1+2d,...,1+100d$ from their mean is $255$ then $d$ is equal to

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

Answer 1

Answer: (C)

$10.1$

Since, we know $\overline{x}=\frac{\text{sum of quantities}}{n}=\frac{n/2(a+l)}{n}$

$=\frac{1}{2}[1+1+100d]=1+50d$

$MD=\frac{1}{n}\sum |x_i-\overline{x}|$

$\Rightarrow 255=\frac{1}{101}[50d+49d+...+d+0+d+...+50d]$

$\Rightarrow 255=\frac{2d}{101}\left[\frac{50\times 51}{2}\right]$

$\therefore d=\frac{255\times 101}{50\times 51}=10.1$