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CA Foundation · Quantitative Aptitude · Correlation and Regression

Two judges awarded marks to five candidates C1 to C5. Judge A: 82, 75, 91, 68, 60. Judge B: 70, 64, 88, 72, 55. Ranking the highest mark as 1 for each judge, what is Spearman's rank correlation coefficient?

The coefficient is 0.70. The ranks are A: 2, 3, 1, 4, 5 and B: 3, 4, 1, 2, 5, which gives Σd² = 6. Then r = 1 − 6×6/(5×24) = 1 − 0.3 = 0.70. The value 0.30 forgets to subtract from 1.

  1. A0.30
  2. B0.60
  3. C0.90
  4. D0.70Correct

Explanation

Judge A ranks: 2, 3, 1, 4, 5. Judge B ranks: 3, 4, 1, 2, 5. The differences are −1, −1, 0, 2, 0, so Σd² = 1+1+0+4+0 = 6. Then r = 1 − 36/120 = 0.70. The value 0.30 is just 36/120 without subtracting from 1.

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