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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Mathematics
Chapter
Statistics

JEE Main 2006 · Mathematics · Statistics

Suppose a population A has 100 observations 101,102, , 200 , and...

Suppose a population AA has 100 observations 101,102,…,200101,102, \ldots, 200, and another population BB has 100 observations 151,152,…,250151,152, \ldots, 250. If VAV_A and VBV_B represent the variances of the two populations, respectively, then VAVB\frac{V_A}{V_B} is

Options

  1. A1
  2. B9/4
  3. C4/9
  4. D2/3

Correct answer

A. 1

Step-by-step solution

σx2=∑d12n\sigma_x^2=\frac{\sum d_1^2}{n}. (Here deviations are taken from the mean) Since AA and BB both has 100 consecutive integers, therefore both have same standard deviation and hence the variance. ∴VAVB=1(\therefore \frac{V_A}{V_B}=1\left(\right. As ∑di2\sum d_i^2 is same in both the cases).
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