# Distribution - Quantile Analysis

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

## 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

$f_i = \frac{\displaystyle i-0,5}{\displaystyle n}$

where:

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