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.


measures of location - percentile - level 1 CFA Exam Review

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






About Soleadea:

Our CFA Exam Study Planner is available to candidates of all levels at groundbreaking Pay-What-You-Can prices. You decide how much you want to pay for our services. After you activate your account, you get unlimited access to our Study Planner 4.0 with study lessons inside, various level 1/level 2 study materials & tools, regular review sessions, and a holistic growth approach to your preparation. Join