Consider the following for the two (02) items that follow: 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 X = 200, Y = 250, X^2 = 900 and Y^2 = 1400. Which one of the following is correct?
B. Variance (X) < Variance (Y)
Given n = 50, X = 200, Y = 250, X^2 = 900, and Y^2 = 1400. The variance of X is calculated as: Var (X) = X^2 n - ( X n )^2 Var (X) = 900 50 - ( 200 50 )^2 Var (X) = 18 - (4)^2 = 18 - 16 = 2 The variance of Y is calculated as: Var (Y) = Y^2 n - ( Y n )^2 Var (Y) = 1400 50 - ( 250 50 )^2 Var (Y) = 28 - (5)^2 = 28 - 25 = 3 Comparing the variances, we get Var (X) Answer: Variance (X) < Variance (Y)
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