Question

If the variance of $1,2,2,3$ is $\lambda ,$ then the value of $log_{2}\lambda $ is

• A. $8$
• B. $1$
• C. $-1$
• D. $-2$

Answer 1

Answer: (C)

We have $n=4,x_{1}=1,x_{2}=2,x_{3}=2,x_{4}=3$ Variance $=\frac{\displaystyle \sum x_{i}^{2}}{n}-\left(\frac{\displaystyle \sum x_{i}}{n}\right)^{2}$

$9$

$\displaystyle \sum x_{i}=8\displaystyle \sum x_{i}^{2}=18$
Variance $=\frac{18}{4}-\left(\frac{8}{4}\right)^{2}$
$=\frac{9}{2}-4=\frac{1}{2}$