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A data consists of n observations `x_(1), x_(2), ..., x_(n). If underset(i = 1)overset(n)Sigma (x_(i) + 1)^(2) = 9n and underset(i = 1) overset(n) Sigma(x_(i) - 1)^(2) = 5n`, then the standard deviation of this data is

A

5

B

2

C

`sqrt(7)`

D

`sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sum_(i=1)^(n)x_(i)^(2)+2sum_(i=1)^(n)x_(i)=8n`
`sum_(i=1)^(n)x_(i)^(2)-2sum_(i=1)^(2)-2sum_(i=1)^(n)x_(i)=4n`
`sum_(i=1)^(n)x_(i)^(2)=6n" : "sum_(i=1)^(n)x_(i)=n`
`"Mean "(sum_(i=1)^(n)(x_(i))/(n))=1" Variance "=sum_(i=1)^(n)((x_(i)1)^(2))/(n)=5" : S.D. "=sqrt5`
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