Concept 6: Quartiles, Quintiles, Deciles, & Percentiles | IFT World

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101 Concepts for the Level I Exam

# Concept 6: Quartiles, Quintiles, Deciles, & Percentiles

A quantile is a value at or below which a stated fraction of the data lies. Some examples of quantiles include:

• Quartiles: distribution is divided into quarters
• Quintiles: distribution is divided into fifths.
• Deciles: distribution is divided into tenths.
• Percentile: distribution is divided into hundredths.

The formula for the position of a percentile in a data set with n observations sorted in ascending order is:

Ly = (n+1) y /100

Calculate the first quartile of a distribution that consists of the following portfolio returns:

3%, 4%, 6%, 9%, 11%, 12%, 14%

Solution:

The first quartile = (7+1) 25/100 = 2nd item in the data set (4%). i.e. 25% of the observations lie below the second observations from the left.

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