Question

Suppose a population A has 100 observations 101, 102, ............., 200 and another population B has 100 obsevrations 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

Answer: (A)

$\sigma^{2}_{x} = \frac{\sum d_{1}^{2}}{n} $ (Here deviations are taken from the mean).
Since A and B both have 100 consecutive integers, therefore both have same standard deviation and hence the variance.
$\therefore \, \frac{V_A}{V_B} = 1$
(As $\sum d_i^2$ is same in both the cases)