The first group of two samples has 100 items with mean15 and SD 3. If the combined sample of two groups, has 250 items with mean 15.6 and  $SD=\sqrt{13.44}$  then SD of the second group is

Use  ${\sigma }^2=\frac{n_1({\sigma }_1^2+d_1^2)+n_2({\sigma }_2^2+d_2^2)}{n_1+n_2}$
Where  $d_1=m_1-a,d_2=m_2-a,a$  being the mean of the whole group, Let  $m_2=$mean of the second group
$15.6=\frac{100\times 15+150\times m_2}{250}\Rightarrow m_2=16$
$(100\times 9+150\times {\sigma }^2)$

Thus,  $13.44=\frac{+100\times {\left(0.6\right)}^2+150\times {\left(0.4\right)}^2}{250}$
$\Rightarrow \sigma =4$