Introduction
Quantiles
Instruction
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 |
