CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A sorted data set contains 19 annual returns (%). Using the position formula L_y = (n + 1) × y/100, the 20th percentile is located at position:
The 20th percentile is located at position 4.0. Using L = (n + 1) × y/100 with n = 19 gives 20 × 0.20 = 4, so it is the fourth ordered observation. Omitting the +1 would give 3.8, which is wrong.
- A3.8Correct
- B4.0
- C3.0
Explanation
L = (19 + 1) × 20/100 = 4.0, so the 20th percentile is the 4th observation. Position 3.8 comes from using n × y/100 = 3.8, which omits the +1. Position 3.0 results from using n-1 in place of n+1, which is wrong. The question asks for the location, which is 4.0.
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