Question

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1,3$ and $8$, then a ratio of other two observations is?

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

Answer 1

Answer: (A)

$4:9$

Let two observations are $x_1$ & $x_2$
mean $=\frac{\sum x_i}{5}=5\Rightarrow 1+3+8+x_1+x_2=25$
$\Rightarrow x_1+x_2=13$ .$\left(1\right)$
variance $\left({\sigma }^2\right)=\frac{\sum x_i^2}{5}-25=9.20$
$\Rightarrow \sum x_i^2=171$
$\Rightarrow x_1^2+x_2^2=97$ ..$\left(2\right)$
by $\left(1\right)$ & $\left(2\right)$
$(x_1+x_2{)}^2-2x_1{x}_2=97$
or $x_1{x}_2=36$
$\therefore x_1:x_2=4:9$.