The mean of five observation is 4 and their variance is 5.2 . If three of these observations are 1,2 and 6, then the other two are,

Options

A. 2 and 9
B. 3 and 8
C. 4 and 7
D. none of these

Answer

3

Explanation

Let two unkown observation are x and y
`barx= 4 = (1 + 2 +6 + x+y)/(5)`
`x + y = 11" "...(1)`
`sigma= 5.2`
`(1^(2)+2^(2) +6^(2) +x^(2) + y^(2))/(5) -(barX)^(2) = 5.2`
`x^(2)+ y^(2) = 65" "...(2)`
by (1) and (2)
`x = 4, y= 7`
or ` x= 7, y = 4`