Calculate the variance and standard deviation for the following discrete frequency distribution:

Here $N=\sum fi=30$

Mean $\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{N}=\frac{420}{30}=14$

and variance  $\left({\sigma }^2\right)=\frac{\sum f_i{\left(x_i-\overline{x}\right)}^2}{N}=\frac{1374}{30}=45.8$

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