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

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

A

9

B

4

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Key idea standard deviation is remain is remain unchanged, if observations are odded or subtracted by a fixed number
We have,
`sum_(i=1)^(9) (x_(1)-5)=9 and sum_(i=1)^(9)(x_(i)-5)^(2)=45`
`SD=sqrt ((sum_(i=1)^(9)(x_(1)-5)^(2))/(9)-((sum_(i=1)^(9)(x_(i)-5))/(9))^(2))`
`rArr SD=sqrt((45)/(9)-((9)/(9))^(2))rArr SD = sqrt(5-1)=sqrt(4)=2`
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