Find the standard deviation for the following data:
 

 

$\begin{array}{r}N=30,\sum _{i=1}^7 f_i{x}_i=420,\sum _{i=1}^7 f_i{\left(x_i-\overline{x}\right)}^2=1374\\ \text{ Therefore, }\overline{x}=\frac{\sum _{i=1}^7 f_i{x}_i}{N}=\frac{1}{30}\times 420=14\end{array}$

$\text{ Hence, variance }\left({\sigma }^2\right)$

$=\frac{1}{N}\sum _{i=1}^7 f_i{\left(x_i-\overline{x}\right)}^2=\frac{1}{30}\times 1374=45.8$

$\text{ and Standard deviation }\left(\sigma \right)=\sqrt{45.8}=6.77$