Which one of the following is correct?
Consider the following for the two (02) items that follow :<br>The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical tubers are given as \Sigma X=200, \Sigma Y=250, \Sigma X^{2}=900 and \Sigma Y^{2}=1400.
- A. Variance (X) > Variance (Y)
- B. Variance (X) < Variance (Y) ✓
- C. Variance (X) = Variance (Y)
- D. Cannot be determined from the given data
Correct Answer: B. Variance (X) < Variance (Y)
Explanation
\text{Variance}(X) = \frac{\Sigma X^2}{n} - (\frac{\Sigma X}{n})^2 = \frac{900}{50} - (\frac{200}{50})^2 = 18 - 16 = 2. \text{Variance}(Y) = \frac{\Sigma Y^2}{n} - (\frac{\Sigma Y}{n})^2 = \frac{1400}{50} - (\frac{250}{50})^2 = 28 - 25 = 3. Hence, \text{Variance}(X) \lt \text{Variance}(Y).
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