# Measures of Location: Computing Percentile

CFA® exam: review / Measures of Location: Percentile

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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