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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29