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?

Answer

12

Explanation

Mean of a,b,8, 5, 10 is 6
`implies (a+b+8 + 5 + 10)/(5) = 6`
`implies a+b = 7`
Variance of a,b,8,5, 10 is 6.80
`implies ((a-6)^2 + (b-6)^2 + (8-6)^2 +(5-6)^2 + (10-6)^2)/(5) = 6.80`
`implies a^2 - 12a + 36 + (1-a)^2 + 21 = 34`
[using eq. (i)]
`implies 2a^2 - 14a + 24 = 0 implies a^2 - 7a + 12 =0`
`implies a= 3 ` or ` 4implies b= 4` or 3