Question

Suppose a population $A$ has 100 observations $101,102,....,200$ and another population $B$ has 100 observations $151,152,153,....,250$. 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 $1$

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