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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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