If the standard deviation of the numbers - 1,0, 1, k is 5 where k >...

$S . D . = \sqrt{\dfrac{∑ {x}_{i}^{2}}{n} - {\left(\dfrac{∑ {x}_{i}}{n}\right)}^{2}} = \sqrt{5}$

$⇒ \dfrac{∑ {x}_{i}^{2}}{n} - {\left(\dfrac{∑ {x}_{i}}{n}\right)}^{2} = 5$

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

$⇒ \dfrac{2 + {k}^{2}}{4} - \dfrac{{k}^{2}}{16} = 5$

$⇒ \dfrac{8 + 4{k}^{2} - {k}^{2}}{16} = 5$

$⇒ 8 + 3{k}^{2} = 80$

$⇒ 3{k}^{2} = 72$

${⇒ k}^{2} = 24$

$⇒ k = \pm 2\sqrt{6}$

Since, $k > 0$

$⇒ k = 2\sqrt{6} .$