Mean of numbers a, b, 8, 5, 10 is 6 and variance is 6.80. Then which one of following gives possible

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13.Statistics

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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 $b$ $?$

A

$a=0 ,b=7$

B

$a=5 ,b=2$

C

$a=1 ,b=6$

D

$a=3 ,b=4$

(AIEEE-2008)

Solution

$6.80=\frac{(6-a)^{2}+(6-b)^{2}+(6-8)^{2}+(6-5)^{2}+(6-10)^{2}}{5}$

$\Rightarrow(6-a)^{2}+(6-b)^{2}+4+1+16=34$

$(6-a)^{2}+(6-b)^{2}=34-21$

$(6-a)^{2}+(6-b)^{2}=13$

$(6-a)^{2}+(6-b)^{2}=9+4$

$(6-a)^{2}+(6-b)^{2}=3^{2}+2^{2}$

$(6-a)^{2}=3^{2}(6-b)^{2}=2^{2}$

$6-a=3 \quad 6-b=2$

$-a=-3 \quad-b=-4$

$a=3$

$b=4$

Standard 11

Mathematics

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