Consider the following the given data,we get Mean =E(x) =
10
∑
i=1
xi
10
=4 =Var(x)=E(x2)−E(x)2 =E(x2)−42=2 ∴E(x)2=18 Hence the new mean will be, E(x)′=
2x1+2x2+2x3....+2x10
10
=2(
x1+x2+x3...x10
10
) =2(
10
∑
i=1
xi
10
) =8 Now the new mean of the square of the observation will be E(x2)′
E(x2)′=
(2x1)2+(2x2)2+(2x3)2....+(2x10)2
10
=4(x12+x22+..x102)
10
=4E(x2) =4(18) =72 Hence the new variance will be equal to Var(x)′ =E(x2)′−E(x)2′ 72−82 72−64 =8 Therefore the mean and variance of the new set of data are 8 and 8 respectively.