The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1,3 and 8, then a ratio of other two observations is

Options

A. `6:7`
B. `4:9`
C. `3:8`
D. `10:3`

Answer

C

Explanation

Let the other two no. be x and y
Mean ` = 5 = (1 + 4 + 9 + x + y)/( 5)`
` x + y = 11`
variance ` = sigma^2 = (sum (x_i - x)^(-2) )/(5)`
` 9.2 xx 5 = (1-5)^2 + (4-5)^2 + (9-5)^2 + (x-5)^2 + (y - 5)^2`
` 46 = 16 + 1 + 16 + (x - 5)^2 + (y - 5)^2`
xy = 24 " " therefore x : y = 3:8`