# Distribution - Quantile Analysis

## 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

## Articles Related

## Special Quantile Name

### Median

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

### 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

## Function

Cleveland’s formula on an ordered data set

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

where:

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