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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`

A

a=0, b=7

B

a=5, b=2

C

a=1, b =6

D

a=3, b=4

Text Solution

Verified by Experts

The correct Answer is:
D
The mean of a, b, 8, 5, and 10 is 6.
`(a+b+8+5+10)/(5)=6`
`implies a+b=7`
Given that the variance is 6.8.
Variance`=(sum(X_(i)-A)^(2))/(n)`
`=((a-6)^(2)+(b-6)^(2)+4+1+16)/(5)=6.8`
`implies a^(2)+b^(2)=25`
`implies a^(2)+(7-a)^(2)=25`
`implies a^(2)-7a+12=0`
`therefore a=4,3 " and" b=3,4`
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