Mathematics - Statistics Question with Solution | TestHub

$$\begin{array}{rl}& \text{ Mean }(\bar{x})=\frac{\text{ sum of quantities }}{n}=\frac{\frac{n}{2}(a+1)}{/n}=\frac{1}{2}[1+1+100d]=1+50d\\ & \text{ M.D. }=\frac{1}{n}\sum \left|x_i-\bar{x}\right|\Rightarrow 255=\frac{1}{101}[50d+49d+48d+\dots .+d+0+d+\dots \dots +50d]=\frac{2d}{101}\left[\frac{50\times 51}{2}\right]\\ & \Rightarrow d=\frac{255\times 101}{50\times 51}=10.1\end{array}$$