Question

The mean of five observations is $5$ and their variance is $\mathrm{9.20.}$ 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)

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