Mathematics - Statistics Question with Solution | TestHub

Let rest two observations are $x$ and $y$.

Given mean $=4$

$\Rightarrow \frac{3+4+4+x+y}{5}=4\Rightarrow x+y=9 ...\left(1\right)$

Given variance $=5.2$

$\Rightarrow \frac{9+16+16+x^2+y^2}{5}-{\left(4\right)}^2=5.2$

$\Rightarrow x^2+y^2=65 ...\left(2\right)$

Squaring equation $\left(1\right)$ and subtracting equation $\left(2\right)$, we get

$2xy=81-65\Rightarrow 2xy=16\Rightarrow xy=8$

$\therefore {\left(x-y\right)}^2=x^2+y^2-2xy=65-16=49$

$\therefore \left|x-y\right|=7$