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`

Options

A. 1
B. `9//4`
C. `4//9`
D. `2//3`

Explanation

`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.)