Suppose a population A has 100 observations 101, 102, ............., 200 and another population B has 100 obsevrations 151, 152, ................ 250. If VA and VB represent the variances of the two populations, respectively then (VA/VB) is

Question

Suppose a population A has 100 observations 101, 102, ............., 200 and another population B has 100 obsevrations 151, 152, ................ 250. If VA and VB represent the variances of the two populations, respectively then (VA/VB) is (A) 1 (B) (9/4) (C) (4/9) (D) (2/3)

Tardigrade Admin · Accepted Answer

σ2x = (∑ d12/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. ∴ (VA/VB) = 1 (As ∑ di2 is same in both the cases)

Q. 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

1

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{2}{3}$

$σ_{x}^{2} = \frac{\sum d _{1}^{2}}{n}$ (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.
$∴ \frac{V _{A}}{V _{B}} = 1$
(As $\sum d_{i}^{2}$ is same in both the cases)

Q. Suppose a population A has 100 observations 101, 102, ............., 200 and another population B has 100 obsevrations 151, 152, ................ 250. If VA​ and VB​ represent the variances of the two populations, respectively then VB​VA​​ is

1

49​

94​

32​

σx2​=n∑d12​​ (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. ∴VB​VA​​=1 (As ∑di2​ is same in both the cases)

Q. 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

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{2}{3}$

$σ_{x}^{2} = \frac{\sum d _{1}^{2}}{n}$ (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.
$∴ \frac{V _{A}}{V _{B}} = 1$
(As $\sum d_{i}^{2}$ is same in both the cases)