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13.Statistics
medium
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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