Question

If sample A contains 100 observations 101, 102, .... 200 and sample B contains 100 observations 151, 152, .... 250, then the ratio of variance \( \frac{V_A}{V_B} \) is:

• A. \( \frac{9}{4} \)
• B. \( \frac{4}{9} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{2}{5} \)

Hint:

The variance of a sample can be calculated by finding the average of squared deviations from the mean.

Answer 1

The Correct Option is A

Step 1: Find the variances of the two samples.
The variance of a sample is given by the formula: \[ V = \frac{\sum (x - \bar{x})^2}{n-1} \] By applying this formula to both samples and simplifying, we find the ratio of the variances to be \( \frac{9}{4} \).
Thus, the correct answer is (1).