NDA 2025 · PYQ · Statistics / Coefficient of variation · medium
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 ΣX = 200, ΣY = 250, ΣX² = 900 and ΣY² = 1400. Which one of the following statements is correct?
A.Coefficient of variation of X is strictly more than coefficient of variation of Y.
B.Coefficient of variation of X is strictly less than coefficient of variation of Y.✓ Correct
C.Coefficient of variation of X is same as coefficient of variation of Y.
D.Coefficient of variation cannot be determined from the given data.
Explanation
Mean(X) = 4, SD(X) = √2 ≈ 1.414, CV(X) = (1.414/4)·100 ≈ 35.36%. Mean(Y) = 5, SD(Y) = √3 ≈ 1.732, CV(Y) = (1.732/5)·100 ≈ 34.64%. Wait, CV(X) > CV(Y). Re-checking: CV(X) = √2/4 ≈ 0.354 and CV(Y) = √3/5 ≈ 0.346. So CV(X) > CV(Y) strictly. The correct option would be (a). However if the official key marks (b), the calculation may differ; based on standard work, (a) is the answer.
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