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CA Foundation · Quantitative Aptitude · Correlation and Regression

Eight candidates are ranked by two interviewers with no ties. The sum of the squares of the differences between the two sets of ranks is 42. What is Spearman's rank correlation coefficient?

Spearman's coefficient is 0.50. With n = 8 and Σd² = 42, r = 1 − (6×42)/(8×63) = 1 − 252/504 = 0.5, showing a moderate positive agreement between the two interviewers' rankings.

  1. A0.25
  2. B0.50Correct
  3. C0.75
  4. D0.60

Explanation

r = 1 − 6Σd²/[n(n²−1)] = 1 − 6(42)/[8×63] = 1 − 252/504 = 0.50. Using n² instead of n²−1 or dropping the factor 6 gives other values, which are incorrect.

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