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The mean and variance of eight observati...

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

Text Solution

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`6,7,10,12,12,13,a,b`
`bar x = (sum x_i)/n `
`(60+a+b)/8 = 9`
`a+b = 12`
`sigma^2 = (sum(x - bar x)^2)/n`
`= (3^2 + 4 + 1 + 9 + 16 + (a-9)^2 + (b-9)^2)/8`
`= 9.25`
`39+(a-9)^2+(b-9)^2=74`
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