Level 1 CFA® Exam: Measures of Location (Computing Percentile)

CFA exam review / Measures of Location: Percentile

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 get a useful piece of advice related to measures of location, recall an important formula, and take a practical tip.

Remember!

Before computing any measure of location (like percentile, median, etc.), sort observations in ascending or a descending order.

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.

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: 1 April 2022