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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression

For a set of paired data, the covariance between X and Y is 12, the standard deviation of X is 4 and the standard deviation of Y is 5. What is the correlation coefficient between X and Y?

The correlation coefficient equals covariance divided by the product of the two standard deviations. Here that is 12 divided by 4 times 5, or 12 divided by 20, which equals 0.6. This is a valid value, since a correlation coefficient must lie between -1 and +1.

  1. A0.6Correct
  2. B2.4
  3. C3.0
  4. D1.33

Explanation

r = Cov(X,Y)/(σx σy) = 12/(4×5) = 12/20 = 0.6. Dividing by only σy gives 2.4, and dividing by only σx gives 3.0. Both of those exceed 1, which is impossible for a correlation coefficient.

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