Question

Suppose population $A$ has $100$ observations $101,102,...200$ and another population $B$ has $100$ observations $151,152,...,250$. If $V_A$ and $V_B$ represents the variance of the two population respectively, then $\frac{V_A}{V_B}$ is equal to

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

Answer 1

The correct option is D

$1$

Explanation for the correct option:

Finding the ratio of the variance of both the observations:

As we know,

$𝜎x^2=\frac{\sum d{i}^2}{n}$ (Here deviations are taken from the mean).

Here$A$ and $B$ both have $100$ consecutive integers, therefore both have the same standard deviation and hence the variance.

So,

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

Therefore option (D) is correct.