Question

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.

Answer 1

`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`
`a^2 + b^2 - 18(a+b) + 162= 35`
`a^2 + b^2 - 216 + 162= 26`
`a^2 +b^2=80 ` eqn(1)
`a+b= 12` eqn(2)
when a=8 , b=4
when a=4, b=8