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 statements is correct?
A. Coefficient of variation of X is strictly more than coefficient of variation of Y.
Mean of X, X = X n = 200 50 = 4 Mean of Y, Y = Y n = 250 50 = 5 Variance of X, _X^2 = X^2 n - ( X )^2 = 900 50 - 4^2 = 18 - 16 = 2 Standard deviation of X, _X = 2 Variance of Y, _Y^2 = Y^2 n - ( Y )^2 = 1400 50 - 5^2 = 28 - 25 = 3 Standard deviation of Y, _Y = 3 Coefficient of variation of X, CV_X = _X X 100 = 2 4 100 = 25 2 35.35\% Coefficient of variation of Y, CV_Y = _Y Y 100 = 3 5 100 = 20 3 34.64\% Since 35.35\% > 34.64\%, the coefficient of variation of X is strictly more than the coefficient of variation of Y. Answer: Coefficient of variation of X is strictly more than coefficient of variation of Y.
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