Question

Mean of five observations is $4.4$ and variance is $8.24$. If three of the observations are $1,2$ and $6$, then the other two observations are

• A. $9,4$
• B. $8,5$
• C. $10,3$
• D. $7,6$

Answer 1

The correct option is A $9,4$

Let the other two observations are $x_1,x_2$
Then $\overline{x}=\frac{x_1+x_2+1+2+6}{5}=4.4$
$\Rightarrow x_1+x_2=13\dots \left(1\right)$

${\sigma }^2=8.24=\frac{1}{5}\sum _{i=1}^5{x}_i^2-(\overline{x}{)}^2$
$\Rightarrow 5(8.24+19.36)=\sum _{i=1}^5{x}_i^2$
$\Rightarrow 5\times 27.6=1+4+36+x_1^2+x_2^2$
$\Rightarrow x_1^2+x_2^2=97\dots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,
$x_1=4,x_2=9$
or $x_1=9,x_2=4$