CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
Sorted monthly returns (%) for a fund are: -4, -2, 0, 1, 3, 5, 8, 12, 20. Using the position formula L = (n + 1) × y/100 with linear interpolation where needed, the interquartile range is closest to:
The interquartile range is about 11, so the closest option is 10.5. With n = 9, Q1 sits at position 2.5 giving -1, and Q3 at position 7.5 giving 10. The difference is 11 percentage points.
- A8.5
- B10.5Correct
- C12.0
Explanation
n = 9. Q1 position = 10 × 0.25 = 2.5, between -2 and 0, so Q1 = -1. Q3 position = 7.5, between 8 and 12, so Q3 = 10. Wait: IQR = 10 - (-1) = 11. Position 7.5 lies between the 7th (8) and 8th (12) values, giving 10. The nearest option to 11 is 10.5.
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