Mathematics - Statistics Question with Solution | TestHub

$\mathrm{S}.\mathrm{D}.=\sqrt{\frac{\sum x_i^2}{n}-{\left(\frac{\sum x_i}{n}\right)}^2}=\sqrt{5}$

$\Rightarrow \frac{\sum x_i^2}{n}-{\left(\frac{\sum x_i}{n}\right)}^2=5$

$\Rightarrow \frac{1+1+0+k^2}{4}-{\left(\frac{-1+0+1+k}{4}\right)}^2=5$

$\Rightarrow \frac{2+k^2}{4}-\frac{k^2}{16}=5$

$\Rightarrow \frac{8+4k^2-k^2}{16}=5$

$\Rightarrow 8+3k^2=80$

$\Rightarrow 3k^2=72$

${\Rightarrow k}^2=24$

$\Rightarrow k=\pm 2\sqrt{6}$

Since, $k>0$

$\Rightarrow k=2\sqrt{6}.$