Solution:

Provided, $n=100, \bar{x}=40$ and $\sigma=10$
$\begin{array}{ll}
\therefore \quad & \frac{\Sigma x_{i}}{n}=40 \\
\Rightarrow \quad & \frac{\Sigma x_{i}}{100}=40 \\
\Rightarrow \quad & \Sigma x_{i}=4000
\end{array}$
So now, $\quad$ Corrected $\Sigma x_{i}=4000-30-70+3+27=3930$ The corrected mean $=\frac{2930}{100}=39.3$
Now, $\quad \sigma^{2}=\frac{\Sigma x_{i}^{2}}{n}-\left(\frac{\Sigma x_{i}}{n}\right)^{2}=\frac{\Sigma x_{i}^{2}}{n}-(40)^{2}$
$\begin{array}{ll}
\Rightarrow \quad & 100=\frac{\Sigma x_{i}^{2}}{100}-1600 \\
\Rightarrow \quad & \Sigma x_{i}^{2}=170000
\end{array}$
So now, $\quad$ Corrected $\Sigma x_{i}^{2}=170000-(30)^{2}-(70)^{2}+3^{2}+(27)^{2}=164938$
$\begin{aligned} \therefore \quad \text { Corrected } \sigma=\sqrt{\frac{164938}{100}-(39.3)^{2}}=\sqrt{1649.38-1544.49} &=\sqrt{104.9} \\ &=10.24 \end{aligned}$