CA Foundation · Quantitative Aptitude · Correlation and Regression
Eight sales executives at a Pune firm are ranked on target achievement and on customer ratings, with no tied ranks. The sum of squared rank differences is Σd² = 21. What is Spearman's rank correlation coefficient?
Spearman's coefficient is 0.75. Substituting n = 8 and Σd² = 21 gives 1 − 126/504 = 0.75. The value 0.25 is only the subtracted fraction, so it is wrong, and a positive result shows the two rankings broadly agree.
- A0.25
- B0.75Correct
- C-0.75
- D0.50
Explanation
r = 1 − 6Σd²/[n(n²−1)] = 1 − 6(21)/[8×63] = 1 − 126/504 = 1 − 0.25 = 0.75. The value 0.25 comes from forgetting to subtract the fraction from 1.
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