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The mean of the numbers a, b, 8, 5, 1...

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? (1) `a""=""0,""b""=""7` (2) `a""=""5,""b""=""2` (3) `a""=""1,""b""=""6` (4) `a""=""3,""b""=""4`

Text Solution

Verified by Experts

mean = `(sum x_i)/n`
`= (a+b+8 + 5+10)/5 = 6`
`a+b + 23= 30`
`a+b = 7`
variance=`( sum ( x_i - bar x)^2)/n`
`= ((a-6)^2 + (b-6)^2 + 4 +1 + 16)/5 = 6.8`
`(a-6)^2 + (b-6)^2 + 21= 34`
`(a-6)^2 + (b-6)^2 = 13`
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Knowledge Check

  • If the mean and the variance of the numbers a, b, 8, 5 and 10 are 6 and 6.8 respectively, then the value of a^(3)+b^(3) is equal to

    A
    58
    B
    61
    C
    91
    D
    89

  • If A=[{:(3,4),(5,6),(7,8):}] and B = [{:(3,5,7),(4,6,8):}] . Then which one of following is correct ?

    A
    B is the inverse of A
    B
    B is the adjoint of A
    C
    B is the transpose of A
    D
    None of the above

  • Find the mean of the values: 1,9,7,3,5,5,6,4,2,8, A. 3 B. 4 C. 5 D.6

    A
    D
    B
    C
    C
    B
    D
    A