For two data sets, each of size 5, the variance is given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined dataset is

σ12=4,n1=5,x¯1=2 σ22=5,n1=5,x¯2=4 x¯12=n1x¯1+n2x¯2n1+n2=5×2+5×410=3 d1=(x¯1−x¯2)=−1,d2=(x¯2−x¯12)=1 σ=n1σ12+n2σ22+n1d12+n2d22n1+n2     =5.4+5.5+5.1+5.110=5510=112  ∴σ2=112