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

∵σx2=4 and σy2=5Also, x¯=2 and y¯=4now,Σxi5=2⇒Σxi=10;Σyi=20and σx2=15Σxi2−(x¯)2⇒Σxi2=5(4+4)⇒Σxi2=40and σ2y=15Σyi2−(y¯)2and Σyi2=5(5+16)⇒Σyi2=105 combined mean, σz2=110Σxi2+Σyi2−x¯+y¯22=110(40+105)−9=145−9010=5510=112