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.

Options

A. 45
B. 49
C. 48
D. 40

Answer

C

Explanation

Let the remaining two observations are a and b.
According to the question,
Mean `=(2+4+10+12+14+a+b)/(7)=8`
`rArr 42+a+b=56`
`rArr a+b=14 " …(i)" `
and variance
`=(a^(2)+b^(2)+4+16+100+144+196)/(7)-8^(2)=16`
`rArr (a^(2)+b^(2)+460)/(7)-64=16`
`rArr (a^(2)+b^(2)+460=560 `
`rArr a^(2) +b^(2) =100 " ...(ii) " `
We know that,
`(a+b)^(2)=(a^(2)+b^(2))+2ab`
`rArr (14)^(2)=100 +2ab " [from Eqs. (i) and (ii)]" `
`rArr 196 =100+2ab`
`rArr 2ab=96`
`rArr ab=48`
So, product of remaining two observations is 48.