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 $x=6,y=1$