CA Foundation · Quantitative Aptitude · Correlation and Regression
For a set of paired observations, 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 Karl Pearson's coefficient of correlation?
Karl Pearson's coefficient equals covariance divided by the product of the two standard deviations. Here that is 12 divided by 4 times 5, which is 12/20 = 0.60. Using only one variance in the denominator gives a wrong value.
- A0.60Correct
- B0.48
- C0.75
- D0.03
Explanation
r = Cov(X,Y)/(σx·σy) = 12/(4×5) = 12/20 = 0.60. Dividing by σy² (25) gives 0.48, which is wrong because the denominator must be the product of the two standard deviations. Dividing by σx² (16) gives 0.75, which has the same flaw.
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