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

For 8 pairs of observations without ties, Spearman's rank correlation coefficient is 0.5. What is the sum of the squared rank differences, Σd²?

Σd² is 42. With n = 8, the denominator n(n²−1) is 504. Setting 1 − 6Σd²/504 = 0.5 gives 6Σd² = 252, so Σd² = 42.

  1. A42Correct
  2. B21
  3. C28
  4. D84

Explanation

n(n²−1) = 8 × 63 = 504. From 0.5 = 1 − 6Σd²/504, we get 6Σd²/504 = 0.5, so 6Σd² = 252 and Σd² = 42. The value 252 is what you get if the factor 6 is forgotten, and 84 results from dividing by 3 rather than 6.

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