$\begin{align}  & \overline{x}=\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{21}}+10+15+45+50}{25}=30 \\  & \to {{x}_{1}}+{{x}_{2}}+...+{{x}_{21}}+120=750 \\  & \to {{x}_{1}}+{{x}_{2}}+...+{{x}_{21}}=650 \\  & \to \overline{{{x}_{new}}}=\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{21}}}{21}=\frac{630}{21}=30 \\  & {{\sigma }^{2}}=\frac{\sum\limits_{i=1}^{25}{{{({{x}_{i}}-\overline{x})}^{2}}}}{25}\overset{\sigma =8}{\mathop{=}}\,64\Rightarrow \sum\limits_{i=1}^{25}{{{({{x}_{i}}-\overline{x})}^{2}}}=1600 \\  \end{align}$ 

اما مجموع مربعات انحراف از میانگین چهار داده‌ی ناجور برابر است با:

$ (10-30)^2+(15-30)^2+(45-30)^2+(50-30)^2=1250 $

پس:

$\begin{align}  & 1250+\sum\limits_{i=1}^{21}{{{({{x}_{i}}-\overline{x})}^{2}}}=1600 \\  & \Rightarrow \sum\limits_{i=1}^{21}{{{({{x}_{i}}-\overline{x})}^{2}}}=350 \\  & \Rightarrow {{\sigma }_{new}}^{2}=\frac{350}{21}\approx 16/66 \\ \end{align}$