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If, s is the standard deviation of the o...

If, `s` is the standard deviation of the observations`x_(1),x_(2),x_(3),x_(4) and x_(5)` then the standard deviation of the observations `kx_(1),kx_(2),kx_(3),kx_(4) and kx_(5)` is

A

`k+s`

B

`s/k`

C

`ks`

D

`s`

Text Solution

Verified by Experts

The correct Answer is:
C
`m=Sigma x_(i)/(5),s=sqrt(Sigmax_(i)^(2)/(5)-((Sigmax_(i))/(5))^(2))`
` therefore " " SD=sqrt((k^(2)Sigmax_(i)^(2))/(5)-((kSigmax_(i))/(5))^2)`
`=sqrt((k^(2)Sigmax_(i)^(2))/5-k^(2)((Sigmax_(i))/5)^(2))=sqrt(((Sigmax_(i)^(2))/(5))-((Sigmax_(i))/5)^(2))=ks`
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