We have, number of terms in the first group n1=100 with their mean X1=15 and number of terms in whole group is n1+n2=250 and their mean X=15.6.
Variance of first groupV1(x)=9 and whole group is Var(x)=13.44.
Now, σ2=n1+n2n1σ12+n2σ22+(n1+n2)2n1n2(xˉ1−xˉ2)2
and n2=150,xˉ2=16,V2(x)=σ2
Therefore, 13.44=250100×9+150×σ22+(250)2100×150×1
⇒σ22=16
⇒σ2=4