Question

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

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

Answer 1

The correct option is C

1

Population B observations are 151, 152, ….., 250
Let y, be these observations
Shifting the origin $z_i=y_i-50$
The values of these observations are 100, 101, ….., 200.
$\therefore V_A=V_B$
( $\because$ Variance is independent of shifting the origin).