$\begin{aligned} & \text { S.D. }=\sqrt{\frac{\sum x_i^2}{n}-(\bar{x})^2} \\ & \Rightarrow 2=\sqrt{\frac{\sum n^2}{n}-\left(\frac{\sum n}{n}\right)^2} \\ & \Rightarrow 4=\frac{n(n+1)(2 n+1)}{6 n}-\left(\frac{n(n+1)}{2 n}\right)^2 \\ & \Rightarrow 4=\frac{n+1}{2}\left\{\frac{2 n+1}{3}-\frac{n+1}{2}\right\} \\ & \Rightarrow 4=\frac{n+1}{2}\left(\frac{n-1}{6}\right) \\ & \Rightarrow n^2=49 \Rightarrow n=7\end{aligned}$