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

Question

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

Tardigrade Admin · Accepted Answer

Since variance is independent of change in origin. Hence variance of observations 101,102, ..... ,200 is same as variance of 151,152, ..., 250 ∴ VA=VB ⇒ (VA/VB)=1

Q. Suppose a population $A$ has 100 observations $101, 102, ..., 200$ and another population $B$ has $100$ observations $151, 152, ..., 250.$ If $V_{A}$ and $V_{B}$ represent the variances of the two population respectively, then $\frac{V _{A}}{V _{B}}$ is :

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{2}{3}$

$1$

Since variance is independent of change in origin. Hence variance of observations 101,102, ..... ,200 is same as variance of 151,152, ..., 250
$∴ V_{A} = V_{B}$
$\Rightarrow \frac{V _{A}}{V _{B}} = 1$

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

49​

94​

32​

1

Since variance is independent of change in origin. Hence variance of observations 101,102, ..... ,200 is same as variance of 151,152, ..., 250 ∴VA​=VB​ ⇒VB​VA​​=1

Q. Suppose a population $A$ has 100 observations $101, 102, ..., 200$ and another population $B$ has $100$ observations $151, 152, ..., 250.$ If $V_{A}$ and $V_{B}$ represent the variances of the two population respectively, then $\frac{V _{A}}{V _{B}}$ is :

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{2}{3}$

$1$

Since variance is independent of change in origin. Hence variance of observations 101,102, ..... ,200 is same as variance of 151,152, ..., 250
$∴ V_{A} = V_{B}$
$\Rightarrow \frac{V _{A}}{V _{B}} = 1$