**Percentiles** and quartiles are specific types of quantiles. More generally, **quantiles** are values that partition (or split) a set of values into approximately **equal-sized** subsets. Common quantiles have special names:

- The 2-quantile is called the
**median**.
- The 4-quantiles are called
**quartiles**.
- The 10-quantiles are called
**deciles**.
- The 100-quantiles are called
**percentiles**.
- The 1,000-quantiles are called
**permilles**.

The formula for **p-th q-quantile** of an n-element set is analogous to the one presented for percentiles:

\lceil\frac{p}{q}n\rceil

Let's calculate the deciles of the following set:

1, 4, 6, 8, 10, 12, 14, 16, 18, 20

There are exactly **10 elements** and **10 deciles**, so each decile corresponds to a single element.

Decile d |
Position |
Decile value |

1^\text{st} |
\lceil\frac{1}{10}10\rceil=\lceil1\rceil=1 |
1 |

2^\text{nd} |
\lceil\frac{2}{10}10\rceil=\lceil2\rceil=2 |
4 |

3^{rd} |
\lceil\frac{3}{10}10\rceil=\lceil3\rceil=3 |
6 |

4^\text{th} |
\lceil\frac{4}{10}10\rceil=\lceil4\rceil=4 |
8 |

5^\text{th} |
\lceil\frac{5}{10}10\rceil=\lceil5\rceil=5 |
10 |

6^\text{th} |
\lceil\frac{6}{10}10\rceil=\lceil6\rceil=6 |
12 |

7^\text{th} |
\lceil\frac{7}{10}10\rceil=\lceil7\rceil=7 |
14 |

8^\text{th} |
\lceil\frac{8}{10}10\rceil=\lceil8\rceil=8 |
16 |

9^\text{th} |
\lceil\frac{9}{10}10\rceil=\lceil9\rceil=9 |
18 |

10^\text{th} |
\lceil\frac{10}{10}10\rceil=\lceil10\rceil=10 |
20 |