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CA Foundation · Quantitative Aptitude · Correlation and Regression

For 10 paired observations of x and y: Σx = 50, Σy = 60, Σxy = 350, standard deviation of x = 2 and standard deviation of y = 3. What is Karl Pearson's coefficient of correlation?

The coefficient is about 0.83. Covariance equals Σxy/n minus the product of the means, which is 35 minus 30, giving 5. Dividing by the product of the standard deviations, 2 times 3, gives r = 5/6, approximately 0.83.

  1. A0.83Correct
  2. B0.60
  3. C1.17
  4. D0.17

Explanation

Mean of x = 5 and mean of y = 6. Covariance = Σxy/n - x̄ȳ = 35 - 30 = 5. r = 5/(2×3) = 5/6 ≈ 0.83. Using 35/ (2×3) without subtracting the product of means gives 5.83, and other options arise from similar slips.

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