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CA Foundation · Quantitative Aptitude · Correlation and Regression

For 8 contestants in a business-quiz final, two judges gave ranks with no ties. The sum of squared rank differences is Σd² = 42. What is Spearman's rank correlation coefficient between the two judges' rankings?

The coefficient is 0.50. Applying R = 1 - 6Σd²/[n(n²-1)] with n = 8 and Σd² = 42 gives 1 - 252/504, which equals 0.5, indicating moderate agreement between the two judges.

  1. A0.50Correct
  2. B-0.50
  3. C1.50
  4. D0.25

Explanation

R = 1 - 6Σd²/[n(n²-1)] = 1 - 6(42)/[8 × 63] = 1 - 252/504 = 0.50. The value -0.50 comes from subtracting in the wrong direction (252/504 - 1 would be -0.5), and 1.50 comes from adding 0.5 to 1 instead of subtracting. Both are wrong, and 1.50 is impossible since R cannot exceed 1.

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