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. 4:09
• B. 6:07
• C. 5:08
• D. 10:03

Answer 1

The Correct Option is 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 $\left(\sigma^{2}\right)=\frac{\sum x _{ i }^{2}}{5}-25=9.20$
$\Rightarrow \quad \sum x_{i}^{2}=171$
$\Rightarrow x _{1}^{2}+ x _{2}^{2}=97$
by $(1) \&(2)$
$\left( x _{1}+ x _{2}\right)^{2}-2 x _{1} x _{2}=97$
or $x _{1} x _{2}=36$
$\therefore x_{1}: x_{2}=4: 9$