The mean of the numbers a,b,8,5,10 is 6 and the variance is 6.80 .Then which one of the following gives possible values of a and b?

Options

A. a=0, b=7
B. a=5, b=2
C. a=1, b =6
D. a=3, b=4

Answer

D

Explanation

The mean of a, b, 8, 5, and 10 is 6.
`(a+b+8+5+10)/(5)=6`
`implies a+b=7`
Given that the variance is 6.8.
Variance`=(sum(X_(i)-A)^(2))/(n)`
`=((a-6)^(2)+(b-6)^(2)+4+1+16)/(5)=6.8`
`implies a^(2)+b^(2)=25`
`implies a^(2)+(7-a)^(2)=25`
`implies a^(2)-7a+12=0`
`therefore a=4,3 " and" b=3,4`