Question

Suppose a population A has 100 observations 101, 102, . . . . 200 and another population B has 100 observations 151, 152, . . . . 250. If $V_A$ and $V_B$ represent the variances of the two populations, respectively then $\frac{V_A}{V_B}$ is

• A. 1
• B. $\frac{9}{4}$
• C. $\frac{4}{9}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A

1

$Variance={\sigma }^2=\frac{1}{n}{\sum }_{i=1}^n(x_i-\mu {)}^2$, where $\mu$ is the mean of the observations.

The difference of an observation and mean of observations of A is same as that of the difference of corresponding observation and mean of observations of B.

So, $V_A=V_B$

$\therefore \frac{V_A}{V_B}=1$