Which one of the following statements 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.

  1. A. Coefficient of variation of X is strictly more than coefficient of variation of Y. ✓
  2. B. Coefficient of variation of X is strictly less than coefficient of variation of Y.
  3. C. Coefficient of variation of X is same as coefficient of variation of Y.
  4. D. Coefficient of variation cannot be determined from the given data.

Correct Answer: A. Coefficient of variation of X is strictly more than coefficient of variation of Y.

Explanation

Mean of X = \frac{200}{50} = 4, Mean of Y = \frac{250}{50} = 5. Standard deviation of X = \sqrt{2} \approx 1.414, SD of Y = \sqrt{3} \approx 1.732. Coefficient of Variation (CV) = \frac{\text{SD}}{\text{Mean}} \times 100. \text{CV}(X) = \frac{\sqrt{2}}{4} \approx 35.35\% and \text{CV}(Y) = \frac{\sqrt{3}}{5} \approx 34.64\%. So, \text{CV}(X) \gt \text{CV}(Y).

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