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If the standard deviation of the numbers...

If the standard deviation of the numbers `-1, 0,1,k` is `sqrt(5)` where `k gt 0` , then k is equal to `2 sqrt(l)` . The value of `l` is ________.

Text Solution

Verified by Experts

The correct Answer is:
6
Since S.D `=sqrt((Sigma x i^(2))/(x)-((Sigmax i )/(x))^(2))=sqrt( ((-1)^(2)+0^(2)+(1)^(2)+K^(2))/(4)-(((-1)+0+(1)+k)/(4))^(2))`
`=sqrt((K^(2)+2)/(4)-(K^(2))/(16)) rArr 3K^(2)+8=16xx5=80`
`=sqrt((3K^(2)+8)/(4)) rArr K^(2)=(72)/(3)=24`
Now, `(sqrt(3K^(2)+8))/(4)=sqrt(5) rArr K=2 sqrt(6)`
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