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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 is correct? Answer
The correct answer is B: Variance (X) < Variance (Y). Variance(X) = ΣX²/n − (ΣX/n)² = 900/50 − (200/50)² = 18 − 16 = 2. Variance(Y) = ΣY²/n − (ΣY/n)² = 1400/50 − (250/50)² = 28 − 25 = 3.
A. Variance (X) > Variance (Y) B. Variance (X) < Variance (Y) ✓ Correct C. Variance (X) = Variance (Y) D. Cannot be determined from the given data Variance(X) = ΣX²/n − (ΣX/n)² = 900/50 − (200/50)² = 18 − 16 = 2. Variance(Y) = ΣY²/n − (ΣY/n)² = 1400/50 − (250/50)² = 28 − 25 = 3. Hence Variance(X) < Variance(Y).
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