1.

If `sum_(i=1)^9 (x_i-5)=9 and sum_(i=1)^9 (x_i-5)^2=45` then the standard deviation of the 9 items `x_1,x_2,.....,x_9` isA. 9B. 4C. 2D. 3

Answer» Correct Answer - 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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