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.