The first of the two samples in a group 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 the second sample is :

n₁ = 100<br><br>m = 250<br><br>$\overline X$₁ = 15<br><br>$\overline X$ = 15.6<br><br>V₁(x) = 9<br><br>Var(x) = 13.44<br><br>$${\sigma ^2} = {{{n_1}\sigma _1^2 + {n_2}\sigma _2^2} \over {{n_1} + {n_2}}} + {{{n_1}{n_2}} \over {{{({n_1} + {n_2})}^2}}}{({\overline x _1} - {\overline x _2})^2}$$<br><br>n₂ = 150, ${\overline x _2}$ = 16, V₂(x) = $\sigma$₂<br><br>$$13.44 = {{100 \times 9 + 150 \times \sigma _2^2} \over {250}} + {{100 \times 150} \over {{{(250)}^2}}} \times 1$$<br><br>$\Rightarrow$ ${\sigma _2}^2$ = 16 $\Rightarrow$ $\sigma$₂ = 4