Consider the first 10 positve integers .If we multiply each number by -1 and then add 1 to each number,the variance of the number so obtained

Options

A. 8.25
B. 6.5
C. 3.87
D. 2.87

Answer

A

Explanation

The first 10 positive integers are 1,2,3,4,5,6,7,8,9 and 10.
On multiplying each number by -1, we get
`-1,-2,-3,-4,-5,-6,-7,-8,-9,-10`
On adding 1 to each number, we get
`0,-1, -2, -3, -4, -5, -6, -7, -8, -9`
`therefore sum x_(i)=(9xx10)/(2)=-45`
and `sum x_(i)^(2)=0^(2)+(-1)^(2)+(-2)^(2)+..+(-9)^(2)=(9xx10xx19)/(6)=285`
`therefore S.D.=sqrt((285)/(10)-((-45)/(10))^(2))=sqrt((285)/(10)-(2025)/(100))`
`=sqrt((2850-2025)/(100))=sqrt(8.25)`
Now, variance `=(S.D.)^(2)=(sqrt(8.25))^(2)=8.25`