Measures of Location: Computing Percentile

CFA® exam: review / Measures of Location: Percentile



measures of location - percentile - level 1 CFA Exam Review

Thanks to this short post, you get a useful piece of advice related to measures of location, recall an important formula and are offered a practical tip.

Remember!

Before computing any measure of location (like percentile, median, etc.), sort observations in an 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 the ascending order: 2, 12, 23, 34, 45, 55, 65, 83, 87 and 89. Determine the value of the 20th percentile.

Solution:

\(n=10\)
\(L_{20}=(n+1)\times\frac{20}{100}=(10+1)\times\frac{20}{100}=2.2\)
\(P_{20}=X_2+(2.2-2)\times(X_3-X_2)=\\=12+0.2\times(23-12)=12+0.2\times11=14.2\)



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