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The covariance between two variables X and Y is 8.4 and their variances are 25and 36 respectively. Calculate Karl Pearson’s coefficient of correlation betweenthem.(a) 0.82(b) 0.28(c) 0.01(d) 0.09

Question

The covariance between two variables X and Y is 8.4 and their variances are 25and 36 respectively. Calculate Karl Pearson’s coefficient of correlation betweenthem.(a) 0.82(b) 0.28(c) 0.01(d) 0.09

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Solution

Karl Pearson’s coefficient of correlation (r) is calculated using the formula:

r = Covariance(X, Y) / sqrt(Variance(X) * Variance(Y))

Given in the question, Covariance(X, Y) = 8.4, Variance(X) = 25, and Variance(Y) = 36.

Substituting these values into the formula, we get:

r = 8.4 / sqrt(25 * 36)

r = 8.4 / sqrt(900)

r = 8.4 / 30

r = 0.28

So, the correct answer is (b) 0.28.

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