Question

The mean and variance of $7$ observations are $8$ and $16$.
If $5$ of these are $2,4,10,12,14$, find the two remaining observations.

• A. $7$ and $7$
• B. $5$ and $8$
• C. $9$ and $3$
• D. $8$ and $6$

Answer 1

The correct option is D $8$ and $6$

Let the two unknown observations be $x$ and $y$.
Mean, $u=8$.
$\Rightarrow u=8=\frac{2+4+10+12+14+x+y}{7}$
$\Rightarrow 42+x+y=56$
$\therefore x+y=14$.... (i)
Now, Variance ${\sigma }^2=16$
$\Rightarrow \frac{2^2+4^2...+x^2+y^2}{7}=16$
$\Rightarrow 460+x^2+y^2=560$
$\therefore x^2+y^2=100$..... (ii)
Solving (i) and (ii) we get,
$x=8,y=6$ or $x=6,y=8$.
Ans-Option $D$.