Given $n=10, \bar{x}=45$ and $\sigma^{2}=16$

$\begin{array}{c}\bar{x}=45 \Rightarrow \frac{\Sigma x_{i}}{n}=45 \\\Rightarrow \quad \frac{\Sigma x_{i}}{10}=45 \Rightarrow \quad \Sigma x_{i}=450 \\\text { Corrected } \Sigma x_{i}=450-52+25=423\end{array}$

$\therefore \quad$ Corrected mean, $\bar{x}=\frac{423}{10}=42.3$

$\Rightarrow \quad \sigma^{2}=\frac{\Sigma x_{i}^{2}}{n}-\left(\frac{\Sigma x_{i}}{n}\right)^{2}$

$\begin{array}{ll}\Rightarrow & 16=\frac{\Sigma x_{i}^{2}}{10}-(45)^{2} \\ \Rightarrow & \Sigma x_{i}^{2}=20410\end{array}$

$\therefore \quad$ Corrected $\Sigma x_{i}^{2}=20410-(53)^{2}+(25)^{2}=18331$

And Corrected $\sigma^{2}=\frac{18331}{10}-(42.3)^{2}=43.81$