The first group of two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation  $\sqrt{13.44}$ then the standard deviation  of second group is

$\begin{array}{l}\text{ Given that }{n}_1=100,\overline{x_1}=15,{\sigma }_1=3,n_2=150\\ n=n_1+n_2=250,\\ \overline{x}=15.6,\sigma =\sqrt{13.44}\end{array}$

$\begin{array}{l}\text{ Further }\overline{x}=\frac{n_1{\overline{x}}_1+n_2{\overline{x}}_2}{n_1+n_2}\\ \Rightarrow 15.6=\frac{100\left(15\right)+150\left({\overline{x}}_2\right)}{250}\\ \Rightarrow {\overline{x}}_2=16\\ d_1={\overline{x}}_1-\overline{x}=15-15.6=-0.6,\\ d_2={\overline{x}}_2-\overline{x}=16-15.6=0.4\\ \text{ We know that }{\sigma }^2=\frac{1}{n_1+n_2}\left[n_1\left({\sigma }_1^2+d_1^2\right)+n_2\left({\sigma }_2^2+d_2^2\right)\right]\\ \Rightarrow (\sqrt{13.44}{)}^2=\frac{1}{250}\left[100\left\{3^2+(-0.6{)}^2\right\}+150\left\{{\sigma }_2^2+(0.4{)}^2\right\}\right]\\ \therefore {\sigma }_2=4\end{array}$

Therefore, the correct answer is (1).