A) \[2\sqrt{\frac{10}{3}}\]
B) \[2\sqrt{6}\]
C) \[4\sqrt{\frac{5}{3}}\]
D) \[\sqrt{6}\]
Correct Answer: B
Solution :
\[S.D=\sqrt{\frac{\Sigma {{\left( x-\overline{x} \right)}^{2}}}{n}}\] \[\overline{x}=\frac{\Sigma x}{4}=\frac{-1+0+1+k}{4}=\frac{k}{4}\] Now\[\sqrt{5}=\sqrt{\frac{{{\left( -1-\frac{k}{4} \right)}^{2}}+{{\left( 0-\frac{k}{4} \right)}^{2}}+{{\left( 1-\frac{k}{4} \right)}^{2}}+{{\left( k-\frac{k}{4} \right)}^{2}}}{4}}\] \[\Rightarrow 5\times 4=2{{\left( 1+\frac{k}{16} \right)}^{2}}+\frac{5{{k}^{2}}}{8}\] \[\Rightarrow \]\[18=\frac{3{{k}^{2}}}{4}\]\[\Rightarrow \]\[{{k}^{2}}=24\]\[\Rightarrow \]\[k=2\sqrt{6}\]
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