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If sum(i=1)^(9) (x(i)-5) " and" sum(i=1)...

If `sum_(i=1)^(9) (x_(i)-5) " and" sum__(i=1)^(9) (x_(i)-5)^(2)=45`, then the standard deviation of the 9 items `x_(1),x_(2),..,x_(9)` is

A

3

B

9

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Let `x_(i)-5=y_(i)`
`therefore underset(i=1)overset(9)(sum y_(i)=9) " and" underset(i=1)overset(9)(sum y_(i)^(2))=45`
So, required standard deviation is
`sigma=sqrt((underset(i=1)overset(9)(sum y_(i)^(2)))/(9)-((underset(i=1)overset(9)(sum y_(i)))/(9))^(2))=sqrt((45)/(9)-((9)/(9))^(2))=2`
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