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Suppose a population A has 100 observati...

Suppose a population A has 100 observations `101,102,................,200` and another population B has 100 observations `151,152,........250.` If `V_A and V_B` represent the variances of the two populations respectively,then `V_A/V_B` is
(a) `1`
(b) `9/4`
(c) `4/9`
(d) `2/3`

A

1

B

`9//4`

C

`4//9`

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
A
`sigma^(2)=(sum d_(i)^(2))/(n)` (Here deviations are taken from the mean.)
Since both A and B have 100 consecutive integers, they have the same standard deviation and hence variance. Therefore,
`(V_(A))/(V_(B))=1 ` (As `sum d_(i)^(2)` is same in both the cases.)
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