Question

The mean and variance of $7$ observations are $7$ and $22$ respectively. If $5$ of the observations are $2,4,10,12,14$ , then the remaining $2$ observations are

• A. $4,3$
• B. $2,5$
• C. $6,1$
• D. $4,2$

Answer 1

Answer: (C)

$\therefore$ Let $x$ and $y$ be remaining $2$ observation
Mean $=7=\frac{2+4+10+12+14+x+y}{7}$
$\Rightarrow x+y=7$ ...(i)
Variance $=22=\frac{1}{7}\left(2^2+4^2+{\left(10\right)}^2+{\left(12\right)}^2+{\left(14\right)}^2+x^2+y^2\right)-{\left(7\right)}^2$
$\Rightarrow x^2+y^2=37$ ...(ii)
Now solving (i) and (ii), we get,
$x=1,y=6$ or $x=6,y=1$