UPSC NDA I 2015 Mathematics Solved Paper

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)′

=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.