Consider the numbers `1,` `2,` `3,` `4,` `5,` `6,` `7,` `8,` `9,` `10`. If `1` is added to each number, the variance of the numbers so obtained is 6.5 (b) 2.87 (c) 3.87 (d) 2.87

Options

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

Answer

D

Explanation

Given numbers are 1,2,3,4,5,6,7,8,9 and 10.
If 1 is added to each number, then observations will be 2,3,4,5,6,7,8,9, 10 and 11.
`therefore sum x_(i)=2+3+4+..+11`
`=(10)/(2)[2xx2+9xx1]=5[4+9]=65`
and `sum x_(i)^(2)=2^(2)+3^(2)+4^(2)+5^(2)+..+11^(2)`
`=(1^(2)+2^(2)+3^(2)+..+11^(2))-(1^(2))`
`=(11xx12xx23)/(6)-1=505`
`therefore s^(2)=(sum x_(i)^(2))/(n)-((sum x_(i))/(n))^(2)=(505)/(10)-((65)/(10))^(2)`
`=50.5-(6.5)^(2)`
`=50.5-42.25`
`=8.25`