Question

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. $a=3,b=4$

Answer 1

The correct option is D

$a=3,b=4$

Mean of $a,b,8,5,10$ is $6$
$\Rightarrow \frac{a+b+8+5+10}{5}=6\Rightarrow a+b=\mathrm{7....}\left(i\right)$
Variance of $a,b,8,5,10$ is $6.80$
$\Rightarrow \frac{(a-6{)}^2+(b-6{)}^2+(8-6{)}^2+(5-6{)}^2+(10-6{)}^2}{5}=6.80$

$\Rightarrow a^2-12a+36+(1-a{)}^2+21=34$ [Using eq.(i)]
$\Rightarrow 2a^2-14a+24=0\Rightarrow a^2-7a+12=0$
$\Rightarrow a=3$ or 4 $\Rightarrow b=4$ or 3
$\therefore$ The possible values of $a$ and $b$ are $a=3$ and $b=4$ or, $a=4$ and $b=3$