CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
Five students scored these marks in Costing (X) and Statistics (Y): (60, 55), (70, 65), (50, 45), (80, 85), (90, 75). Ranking the highest mark as 1 in each subject, what is Spearman's rank correlation coefficient?
The coefficient is 0.9. The ranks differ only for the last two students, by one place each, so Σd² = 2. Then r = 1 − 6×2/120 = 0.9, indicating a strong positive relationship between the two subjects' ranks.
- A0.9Correct
- B0.1
- C0.8
- D0.7
Explanation
X ranks: 4, 3, 5, 2, 1. Y ranks: 4, 3, 5, 1, 2. The differences are 0, 0, 0, 1, −1, so Σd² = 2. r = 1 − 6×2/(5×24) = 1 − 12/120 = 0.9. The value 0.1 comes from stopping at 12/120 and not subtracting it from 1.
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