The first of the two samples in a group has 100 items with mean 15...

We have, number of terms in the first group ${n}_{1} = 100$ with their mean ${X}_{1} = 15$ and number of terms in whole group is ${n}_{1} + {n}_{2} = 250$ and their mean $X = 15 . 6 .$

Variance of first group${V}_{1}\left(x\right) = 9$ and whole group is $Var \left(x\right) = 13 . 44 .$

Now, ${\sigma}^{2} = \dfrac{{n}_{1}{\sigma}_{1}^{2} + {n}_{2}{\sigma}_{2}^{2}}{{n}_{1} + {n}_{2}} + \dfrac{{n}_{1}{n}_{2}}{{\left({n}_{1} + {n}_{2}\right)}^{2}}{\left(\overset{¯}{x}1 - \overset{¯}{x}2\right)}^{2}$

and ${n}_{2} = 150, \overset{¯}{x}2 = 16, {V}_{2} ( x ) = {\sigma}_{2}$

Therefore, $13 . 44 = \dfrac{100 \times 9 + 150 \times {\sigma}_{2}^{2}}{250} + \dfrac{100 \times 150}{{\left(250\right)}^{2}} \times 1$

$⇒ {\sigma}_{2}^{2} = 16$

$⇒ {\sigma}_{2} = 4$