If the mean deviations about the median of the numbers $a, 2a, \dots , 50a$ is $50$, then $\left|a\right|$ equals

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 $4x$.