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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

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The correct Answer is:
12
Mean of a,b,8,5,19 is 6
`rArr(a+b+8+5+10)/5=6`
`rArra+b=7`
Variance of a,b,8,5,10 is 6.80
`rArr((a-6)^(2)+(b-6)^(2)+(8-6)^(2)+(5-6)^(2)+(10-6)^(2))/5=6.80`
`rArra^(2)-12a+36+(1-a)^(2)+21=34`
[using eq. (i)]
`rArr2a^(2)-14a+24=0rArra^(2)-7a+12=0`
`rArra=3` or `4rArrb=4` or 3
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