Find the standard deviation for the following data:
$\begin{array}{cccccc}{x}_i& 3& 8& 13& 18& 23\\ f_i& 7& 10& 15& 10& 6\end{array}$

$\begin{array}{ccccc}{x}_i& f_i& f_i{x}_i& x_i^2& f_i{x}_i^2\\ 3& 7& 21& 9& 63\\ 8& 10& 80& 64& 640\\ 13& 15& 195& 169& 2535\\ 18& 10& 180& 324& 3240\\ 23& 6& 138& 529& 3174\\ & \sum f_i=48& \sum f_i{x}_i=614& & \sum f_i{x}_i^2=9652\end{array}$
As we know,
Std. Deviation $\left(\sigma \right)=\frac{1}{N}\sqrt{N\sum f_i{x}_i^2-(\sum f_i{x}_i{)}^2}$
$=\frac{1}{48}\sqrt{48\times 9652-(614{)}^2}$
$=\frac{1}{48}\sqrt{463296-376996}$
$=\frac{1}{48}\sqrt{86300}$
$=\frac{1}{48}\times 293.77$
$=6.12$