Explanation

(a)
We know, $\sigma^{2} = \frac{n_{1}\left( \sigma_{1}^{2} + d_{1}^{2} \right) + n_{2}(\sigma_{2}^{2} + d_{2}^{2})}{n_{1} + n_{2}}$
Where $d_{1} = m_{1} - a,\ d_{2} = m_{2} - a,\ a$ being the mean of the whole group
$\therefore\ \ 15.6 = \frac{100 \times 15 + 150 \times m_{2}}{250}$
$\Rightarrow \ \ m_{2} = 16$
Thus, $13.44 = \frac{\left\lbrack \left( 100 \times 9 + 150 \times \sigma^{2} \right) + 100 \times (0.6)^{2} + 150 \times (0.4)^{2} \right\rbrack}{250}$
$\Rightarrow \ \ \sigma = 4$