JEE MAIN - Mathematics (2006 - No. 1)
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 populations, respectively, then $${{{V_A}} \over {{V_B}}}$$ is
1
$${9 \over 4}$$
$${4 \over 9}$$
$${2 \over 3}$$
Explanation
Series A = 101, 102 ............ 200
Series B = 151, 152 ............ 250
Here series B can be obtained if we change the origin of A by 50 units.
And we know the variance does not change by changing the origin.
So, $$\,\,\,\,$$ $${V_A} = {V_B}$$
$$ \Rightarrow \,\,\,\,\,{{{V_A}} \over {{V_B}}} = 1$$
Series B = 151, 152 ............ 250
Here series B can be obtained if we change the origin of A by 50 units.
And we know the variance does not change by changing the origin.
So, $$\,\,\,\,$$ $${V_A} = {V_B}$$
$$ \Rightarrow \,\,\,\,\,{{{V_A}} \over {{V_B}}} = 1$$
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