Question

The arithmetic mean of the observations $10,8,5,a,b$ is $6$ and their variance is $6.8$. then $ab=$

• A. $6$
• B. $4$
• C. $3$
• D. $12$

Answer 1

The correct option is D $12$

$\frac{10+8+5+a+b}{5}=6$,
$\Rightarrow a+b=7$
$\frac{1}{n}\sum (x_1-\overline{x}{)}^2=6.8$
$\Rightarrow (6-a{)}^2+(6-b{)}^2=(6.8\times 5)-16-4-1$
put $b=7-a$
$\Rightarrow 36+a^2-12a+1+a^2-2a=13$
$\Rightarrow a^2-7a+12=0$
$\Rightarrow a=3$ or $4$
So, $b=4$ or $3$
Hence, Product $=12$