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CA Foundation · Quantitative Aptitude · Correlation and Regression

Six candidates are ranked by two judges with no tied ranks. Spearman's rank correlation coefficient is found to be -0.2. What is the sum of the squares of the rank differences, Σd²?

Σd² equals 42. For n = 6, n(n²−1) = 210. Setting -0.2 = 1 − 6Σd²/210 gives 6Σd² = 252, so Σd² = 42, which is consistent with a mildly negative rank association.

  1. A35
  2. B28
  3. C42Correct
  4. D49

Explanation

Use r = 1 − 6Σd²/[n(n²−1)] with n(n²−1) = 6×35 = 210. Then -0.2 = 1 − 6Σd²/210, so 6Σd²/210 = 1.2 and Σd² = 42. The value 35 results from forgetting the factor 6 on the numerator.

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