Level 1 CFA® Exam: Measures of Location (Computing Percentile)
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11 months 1 week 6 days
This blog post was created as a part of the CFA exam review series to help you in your level 1 exam revision, whether done regularly or shortly before your CFA exam.
Thanks to this short post, you can recall an important level 1 CFA exam formula and get a useful piece of advice related to measures of location and a practical tip.
Formula for the Location of a Percentile
\(L_y=(n+1)\times\frac{y}{100}\)
- Where:
- \(y\) – percentile,
- \(L_y\) – location of the percentile,
- \(n\) – number of observations.
Remember!
Before computing any measure of location (like percentile, median, etc.), sort observations in ascending or descending order.
Measures of Location: Practical Tip
If the location of the percentile is not an integer, we need to apply linear interpolation to compute this percentile. Have a look at the example.
Example:
There is a set of numbers given in ascending order: 2, 12, 23, 34, 45, 55, 65, 83, 87, and 89. Determine the value of the 20th percentile.
Solution:
\(n=10\)
\(L_{20}=(n+1)\times\frac{20}{100}=(10+1)\times\frac{20}{100}=2.2\)
\(P_{20}=X_2+(2.2-2)\times(X_3-X_2)=\\=12+0.2\times(23-12)=12+0.2\times11=14.2\)
LAST UPDATE: 2 Nov 2023
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