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If mean and standard deviation of 5 observations `x_(1), x_(2), x_(3), x_(4), x_(5)` are 10 and 3, respectively, then the variance of 6 observations `x_(1), x_(2), …, x_(5)` and -50 is equal to

A

507.5

B

509.5

C

586.5

D

582.5

Text Solution

Verified by Experts

The correct Answer is:
A
`mu=(sum x_(i))/(N)=10" " (N=5)`
`therefore sum x_(i)=50`
Standard deviation = 3
`therefore ` variance = 9
`(sum(x_(i)-mu)^(2))/(N)=9`
`therefore sumx_(i)^(2)+sum mu^(2)-2mu sum x_(i)=45`
`sum x_(i)^(2)+100(5)-2xx10xx50=45`
`sum x_(i)^(2)=545`
Mean of `x_(1),x_(2),x_(3), x_(4), x_(5) and -50= (sum x_(i)-50)/(6)=0`
New variance `=(sum x_(i)^(2)+(50)^(2))/(6)=(3045)/(6)=507.5`
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