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Let a, b, c, d, e, be the observations w...

Let `a, b, c, d, e,` be the observations with mean m and standard deviation `s.` The standard deviation of the observations `a+k, b+k, c+k, d+k, e+k` is

A

`s`

B

`ks`

C

`s+k`

D

`s/k`

Text Solution

Verified by Experts

The correct Answer is:
A
Given observation are a,b,c,d and e .
Mean =m`=(a+b+c+d+e)/5 `
`Sigmax_(i)=a+b+c+d+e=5m`
`mean=(a+k+b+k+c+k+d+k+e+k)/5`
`=((a+b+c+d+e)+5k)/5=m+k`
`therefore " " SD=sqrt((Sigma(x_(i)+k)^(2))/n-(m+k)^(2))`
`=sqrt((Sigma(x_(i)^(2)+k^(2)+2kx_(i)))/n-(m^(2)+k^(2)+2mk))`
`sqrt((Sigmax_(i)^(2))/n-m^2+(2kSigmax_(i))/n-2mk)`
`sqrt((Sigmax_(i)^(2))/n-m^(2)+2km-2mk)`
`sqrt((Sigma_(i)^(2))/n-m^(2))`
`s`
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