Question

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.

Answer 1

`sum x_i = 2+4+10+12+14+a+b`
`bar x = (sumx_i)/n`
`(42+a+b)/7 = 8`
`a+b = 14`
`16 = (sum(x_i - bar x)^2)/n = (36 + 16+4+16+36+(a-8)^2 + (b-8)^2)/7 `
`112 = 108 + (a-8)^2 + (b-8)^2 `
`4 = a^2 + b^2 - 2*8*(a+b) + 128`
`4 = a^2 + b^2 -16*14 + 128`
`a^2 + b^2 = 100`
`a+b = 14`
if `a=8 ,`then b= 6
if `a=6,`then b=8
answer