# Statistics - Frequency Tables

A frequency table is a way to present data. The data are counted and ordered to summarize larger sets of data.

With a frequency table you can analyze the way the data is distributed across different values.

## Frequency Tables

Frequency means the number of times a value appears in the data. A table can quickly show us how many times each value appears.

If the data has many different values, it is easier to use intervals of values to present them in a table.

Here is the age of the 934 Nobel Prize winners up until the year 2020. In the table each row is an age interval of 10 years.

Age Interval | Frequency |
---|---|

10-19 | 1 |

20-29 | 2 |

30-39 | 48 |

40-49 | 158 |

50-59 | 236 |

60-69 | 262 |

70-79 | 174 |

80-89 | 50 |

90-99 | 3 |

We can see that there is only one winner from ages 10 to 19. And that the highest number of winners are in their 60s.

**Note:** The intervals for the values are also called 'bins'.

## Relative Frequency Tables

Relative frequency means the number of times a value appears in the data compared to the total amount. A **percentage** is a relative frequency.

Here are the relative frequencies of ages of Noble Prize winners. Now, all the frequencies are divided by the total (934) to give percentages.

Age Interval | Relative Frequency |
---|---|

10-19 | 0.11% |

20-29 | 0.21% |

30-39 | 5.14% |

40-49 | 16.92% |

50-59 | 25.27% |

60-69 | 28.05% |

70-79 | 18.63% |

80-89 | 5.35% |

90-99 | 0.32% |

## Cumulative Frequency Tables

Cumulative frequency counts up to a particular value.

Here are the cumulative frequencies of ages of Nobel Prize winners. Now, we can see how many winners have been younger than a certain age.

Age | Cumulative Frequency |
---|---|

Younger than 20 | 1 |

Younger than 30 | 3 |

Younger than 40 | 51 |

Younger than 50 | 209 |

Younger than 60 | 445 |

Younger than 70 | 707 |

Younger than 80 | 881 |

Younger than 90 | 931 |

Younger than 100 | 934 |

Cumulative frequency tables can also be made with relative frequencies (percentages).