Distribution - Quantile Analysis

1 - About

A quantile is a statistic that identifies the data that is less than the given value (ie that fall at or below a score in a distribution).

A quantile function will always rank the data before giving any output.

The quantile limits can be use to create equal-frequency bins

3 - Special Quantile Name

3.1 - Median

The most commonly used percentile is the median. Half of the data is below the median.

3.2 - List

  • The only 2-quantile is called the median
  • The 3-quantiles are called tertiles or terciles
  • The 4-quantiles are called quartiles
  • The 5-quantiles are called quintiles
  • The 6-quantiles are called sextiles
  • The 7-quantiles are called septiles
  • The 8-quantiles are called octiles
  • The 10-quantiles are called deciles
  • The 12-quantiles are called duo-deciles
  • The 16-quantiles are called hexadeciles
  • The 20-quantiles are called ventiles or vigintiles
  • The 100-quantiles are called percentiles
  • The 1000-quantiles are called permilles

4 - Function

Cleveland’s formula on an ordered data set

<math> f_i = \frac{\displaystyle i-0,5}{\displaystyle n} </math>


  • n is the total number of element
  • i is the nth element of an ordered data set

5 - Documentation / Reference

Data Science
Data Analysis
Data Science
Linear Algebra Mathematics

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