Q.19. If the varaince of the numbers -1,0,1,k is 5 where k>0, then k is equal to
A. 2\sqrt{\frac{10}{3}}
B. 2\sqrt{6}
C. 4\sqrt{\frac{5}{3}}
D. \sqrt{6}
Answer :-B. 2\sqrt{6}
Explanation :- Variance equation:
\mathrm{Variance}=\frac{1}{n}\sum_{i=1}^{n}x_{i}^{2}-\bar{x}^{2}Given: n=4 and \mathrm{variance} = 5
5=\frac{1}{4}\left[(-1)^2+(0)^2+(1)^2+k^2\right]-\left(\frac{-1+0+1+k}{4}\right)^2 5=\frac{2+k^{2}}{4}-\frac{k^{2}}{16} 80=8+4k^2-k^2 3k^{2}=72 k^2=24 k=2\sqrt{6} \quad\ldots[\because k>0]