Question

The mean and variance of seven observations are $8$ and $16$ respectiveley. If $5$ of the observations are $2,4,10,12,14,$ then the product of the remaining two observations is:

• A. $40$
• B. $49$
• C. $45$
• D. $48$

Answer 1

The correct option is D $48$

Let remaining two observations be $p$ and $q.$
Mean $=8$
$\Rightarrow \frac{p+q+2+4+10+12+14}{7}=8$
$\Rightarrow p+q=14$

Variance $=16$
$\Rightarrow \frac{p^2+q^2+4+16+100+144+196}{7}-(8{)}^2=16$
$\Rightarrow p^2+q^2=100$

$\Rightarrow pq=\frac{(p+q{)}^2-(p^2+q^2)}{2}$
$=\frac{196-100}{2}$
$=48$