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The mean and variance of 7 observations ...

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

A

48

B

40

C

45

D

49

Text Solution

Verified by Experts

The correct Answer is:
A
Mean `=(a+b+2+4=10+12+14)/(7)=8rArr(a+b+42)/(7)=8`
Variance = 16 `" " a+b+42=56`
`V=(sumx^2)/(N)-mu^2" "a+b=14`
`V=(a^2+b^2+2^2+4^2+10^2+12^2+14^2)/(7)-8^2`
`16=(a^2+b^2+460)/7-64`
`80=(a^2+b^2+460)/7`
`560=a^2+b^2+460`
`a^2+b^2=100`
`a^2+b^2=100`
`(a+b)^2-2ab=100`
`(14)^2-2ab=100`
`196-2ab=100`
`196-100=2ab`
`96/2=abimpliesab=48`
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