Explanation

(b)
$\because\sigma_{x}^{2} = 4and\sigma_{y}^{2} = 5$
Also $\overline{x} = 2\ and\ \overline{y}$=4
Now, $\frac{\Sigma x_{i}}{5} = 2 \Rightarrow \Sigma x_{i} = 10$
$\frac{\Sigma y_{i}}{5} = 4 \Rightarrow \Sigma y_{i} = 20$
Since $\sigma_{x}^{2} = \frac{1}{5}\left( \Sigma x_{i}^{2} \right) - \left( \overline{x} \right)^{2}$
$\Rightarrow \ \Sigma x_{i}^{2} = 40$
Similarly $\Sigma x_{i}^{2} = 105$
$\therefore\sigma_{x}^{2} = \frac{1}{10}\left( \Sigma x_{i}^{2} + \Sigma y_{i}^{2} \right) - \left( \frac{\overline{x} + \overline{y}}{2} \right)^{2}$
$= \frac{1}{10}(40 + 105) - 9$
$= \frac{55}{10} = \frac{11}{2}$