Official solution
\begin{gathered} Var(8,21,34,47,\ldots \ldots ,320) \\ Var(0,13,26,39,\ldots \ldots ,312) \\ {13}^{2}\cdot Var(0,1,2,\ldots \ldots ,24) \\ {13}^{2}\cdot Var(1,2,3,\ldots \ldots ,25) \\ {\sigma }^{2}={13}^{2}\times (\frac{{25}^{2}-1}{12})=8788 \\ \\ 8+(n-1)13=320 \\ 13n=325 \\ n=25
=25 \\ =\frac{\sum {x}_{i}}{n}=\frac{8+21+\ldots +320}{25}=\frac{\frac{25}{2}(8+320)}{25} \\ {\sigma }^{2}=\frac{\sum {x}_{2}^{i}}{n}-({)}^{2} \\ =\frac{{8}^{2}+{21}^{2}+\ldots .+{320}^{2}}{13}-(164{)}^{2} \\ =8788 \end{gathered}