Find the standard deviation of the following continuous frequency distribution

Let the assumed Mean A = 65 

Then $d_i=\frac{x_i-65}{10}$ 

Construed the table

$\overline{x}=A+\left(\frac{\mathrm{\Sigma }{f}_i{d}_i}{N}\right)h=65+\left(\frac{-15}{50}\right)10=65-3=62$

Variance ${\sigma }^2=\frac{h^2}{N}\left[\frac{1}{N}\sum f_i{d}_i^2-{\left(\sum \frac{f_i{d}_i}{N}\right)}^2\right]=\frac{h^2}{N^2}\left[N\sum f_i{d}_i^2-{\left(\sum f_i{d}_i\right)}^2\right]$

${\sigma }^2=\frac{100}{2500}\left[50\left(105\right)-(-15{)}^2\right]=\frac{1}{25}(5250-225)=201$

Standard deviation  $\mathrm{A}=\sigma =\sqrt{201}=14.18\left(\text{ Approximately }\right)$