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

Let $x_1,x_2,..., x_n be n$ observations, and let $x$ be their arithmetic mean and ${\delta }^2$ be the variance

Statement $\mathbf{1}\mathbf{:}$ Variance of $2x_1,2x_2, ...., 2x_n$ is $4{\delta }^2$.

Statement $\mathbf{2}\mathbf{:}$ Arithmetic mean $2x_1,2x_2, ...., 2x_n$ is $4x$.