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 |