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Consider the first 10 positive integers ...

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

A

`8.25`

B

`6.5`

C

`3.87`

D

`2.87`

Text Solution

Verified by Experts

The correct Answer is:
A
Since the first 10 positive intergers are 1,2,3,4,5,6,7,8, 9, and 10 on multiplying by-1 we get
-1,-2,-3,-4,-5,-6,-7,-8,-9,-10
On adding 1 in each number ,we get
0 -1,-2,-3,-4,-5,-6,-7,-8,-9
`therefore " " Sigmax_(i)=0-1-2-3-4-5-6-7-8-9`
`=-(9xx10)/2`
= - 45
`Sigma x_(i)^(2)=0^(2)+(-1)^(2)+(-2)^(2)+...+(-9)^(2)`
`- (9xx10xx190)/(6)`
285
`therefore " " SD =sqrt((285)/10-((-45)/10)^(2))=sqrt(285/10-2025/100)`
`=sqrt((2850-2025)/100)=sqrt(8.25)`
Now variance `=(SD)^(2)=(sqrt(8.25)^(2)=8.25`
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