CA Foundation · Quantitative Aptitude · Correlation and Regression
Five candidates in an aptitude test scored the following marks in Test X: 60, 45, 80, 70, 55 and in Test Y (same order of candidates): 52, 40, 75, 65, 58. Ranking the highest mark as 1, what is Spearman's rank correlation coefficient?
Spearman's coefficient is 0.90. After ranking, the rank differences are -1, 0, 0, 0 and 1, giving Σd² = 2. Then R = 1 - 6×2/(5×24) = 0.9, showing strong agreement between the two tests.
- A0.90Correct
- B0.98
- C0.10
- D0.80
Explanation
X ranks: 3, 5, 1, 2, 4. Y ranks: 4, 5, 1, 2, 3. Differences: -1, 0, 0, 0, 1, so Σd² = 2. R = 1 - 6(2)/(5 × 24) = 1 - 12/120 = 0.90. The value 0.10 results from forgetting to subtract the fraction from 1.
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