The standard deviation of the following distribution \begin{array}{|c|c|c|c|} \hline C.I. & 0-6 & 6-12 & 12-18 \\ \hline \mathrm{f}_{\mathrm{i}} & 2 & 4 & 6 \\ \hline \end{array} is

\begin{array}{|c|c|c|c|c|c|} \hline C.I. & \mathbf{f}_{\mathbf{i}} & \boldsymbol{x}_{\mathbf{i}} & \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} & \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}} & \mathbf{f}_{\mathbf{i}} \boldsymbol{x}_{\mathbf{i}}^{\mathbf{2}} \\ \hline 0-6 & 2 & 3 & 9 & 6 & 18 \\ \hline 6-12 & 4 & 9 & 81 & 36 & 324 \\ \hline 12-18 & 6 & 15 & 225 & 90 & 1350 \\ \hline Total & \mathbf{1 2} & & & \mathbf{1 3 2} & \mathbf{1 6 9 2} \\ \hline \end{array} Here $\sum \mathrm{f}_{\mathrm{i}}=12, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}=132, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}^2=1692$ $\begin{aligned} \therefore \quad \mathrm{V}(\mathrm{X}) & =\frac{1692}{12}-\left(\frac{132}{12}\right)^2 \\ & =141-121 \\ & =20 \end{aligned}$ $\therefore \quad$ Standard deviation $=\sqrt{20}=2 \sqrt{5}$