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. `5:8`
D. `10:3`

Answer

B

Explanation

Let the other two no. be x and y
Mean =5 `=(1+3+8+x+y)/5`
`x+y=13` ….(1)
Variance `=sigma^(2)=(sum(x_(i)-barx)^(2))/5`
`sigma^(2)=((1-5)^(2)+(3-5)^(2)+(8-5)^(2)+(x-5)^(2)+(y-5)^(2))/5`
`9.20xx5=16+4+9+x^(2)+y^(2)-10(x+y)+50`
`x^(2)+y^(2)=97` ....(2)
`(13)^(2)=97+22y`
`2xy=72`
`2xy=72`
`xy=36`
`thereforex:y=4:9`