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The outcome of each of 30 items was obse...

The outcome of each of 30 items was observed, 10 items gave an outcome `(1)/(2)-d` each, 10 items gave outcome `(1)/(2)` each and the remaining 10 items gave outcome `(1)/(2) + d` each. If the variance of this outcome data is `(4)/(3)`, then `|d|` equals

A

`(2)/(3)`

B

`(sqrt(5))/(2)`

C

`sqrt(2)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`sigma^(2)=(Sigmax^(2))/(n)-mu^(2)`
`=(10((1)/(2)-d)^(2)+10xx(1)/(4)+10((1)/(2)+d)^(2))/(30)`
`-((10((1)/(2)-d)+10xx(1)/(2)+10((1)/(2)+d))/(30))^(2)" "[because mu=(Sigma x_(i))/(n)]`
`=(20((1)/(4)+d^(2))+5//2)/(30)-((1)/(4))`
`=((15)/(2)+20d^(2))/(30)-(1)/(4)=(1)/(4)+(2d^(2))/(3)-(1)/(4)=(2)/(3)d^(2)`
` therefore (2)/(3) d^(2)=(4)/(3) rArr d^(2)=2 rArr |d|=sqrt(2)`
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