Introduction
Quantiles
Instruction
Find the percentiles of this set:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... , 99, 100
There are 100 elements in this set. Using the formula \lceil\frac{p}{100}n\rceil we get the results:
| Percentile p | Position | Percentile value |
|---|---|---|
| 5^\text{th} | \lceil\frac{5}{100}100\rceil=5 | 5 |
| 25^\text{th} | \lceil\frac{25}{100}100\rceil=25 | 25 |
| 50^\text{th} | \lceil\frac{50}{100}100\rceil=50 | 50 |
| 70^\text{th} | \lceil\frac{70}{100}100\rceil=70 | 70 |
| 75^\text{th} | \lceil\frac{75}{100}100\rceil=75 | 75 |
Let's try a smaller set:
1, 4, 6, 8, 10, 12, 14, 16, 18, 20
And calculate a few percentiles:
| Percentile p | Position | Percentile value |
|---|---|---|
| 5^\text{th} | \lceil\frac{5}{100}10\rceil=\lceil0.5\rceil=1 | 1 |
| 25^\text{th} | \lceil\frac{25}{100}10\rceil=\lceil2.5\rceil=3 | 6 |
| 50^\text{th} | \lceil\frac{50}{100}10\rceil=\lceil5\rceil=5 | 10 |
| 65^\text{th} | \lceil\frac{65}{100}10\rceil=\lceil6.5\rceil=7 | 14 |
| 70^\text{th} | \lceil\frac{70}{100}10\rceil=\lceil7\rceil=7 | 14 |
| 75^\text{th} | \lceil\frac{75}{100}10\rceil=\lceil7.5\rceil=8 | 16 |
