1.

Themean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then whichone of the followinggivespossible 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`

Answer» 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`
`(a-6)^2 + (1-a)^2 = 13`
`a^2 - 12a + 36 + 1 - 2a + a^2 = 13`
`2a^2 - 14a + 24= 0`
`a^2 - 7a + 12= 0`
`(a-4)(a-3) = 0`
`a= 4or 3 `
and `b= 3 or 4 `
option 4 is correct


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