Question

If the standard deviation of the numbers $-1,0,1,k$ is $\sqrt{5}$, then $k$ is equal to:

• A. $\sqrt{6}$
• B. 2$\sqrt{\frac{10}{3}}$
• C. 2$\sqrt{6}$
• D. 4$\sqrt{\frac{5}{3}}$

Answer 1

The correct option is C 2$\sqrt{6}$

$Mean=\overline{x}=\frac{\sum x}{n}=\frac{-1+0+1+k}{4}=\frac{k}{4}S.D.=\sqrt{\frac{\sum (x{)}^2}{n}-\overline{x}}=\sqrt{\frac{k^2+2}{4}-\frac{k^2}{16}=}\sqrt{5}\Rightarrow \frac{3k^2+8}{16}=5\Rightarrow k^2=24$