**Frequency** tells you how often a result happens.

**Cumulative frequency **tells you how often a result happens that is less than or equal to the given value.

To find cumulative frequency, we add together the frequencies up to and including the given result.

**Example**

The marks of 30 children in a maths exam were recorded in a table as shown below.

Calculate the cumulative frequencies for each class.

Marks | frequency (f) | Cumulative frequency |
---|---|---|

0 ≤ m ≤ 20 | 2 | |

20 < m ≤ 40 | 5 | |

40 < m ≤ 60 | 11 | |

60 < m ≤ 80 | 8 | |

80 < m ≤ 100 | 4 | |

Total | 30 |

**Answer**

To work out the cumulative frequency for each class interval, add the previous cumulative frequency to the frequency for that class.

Alternatively, add up all the frequencies up to and including that class.

Marks | frequency (f) | Cumulative frequency |
---|---|---|

0 ≤ m ≤ 20 | 2 | 2 |

20 < m ≤ 40 | 5 | 2 + 5 = 7 |

40 < m ≤ 60 | 11 | 7 + 11 = 18 |

60 < m ≤ 80 | 8 | 18 + 8 = 26 |

80 < m ≤ 100 | 4 | 26 + 4 = 30 |

Total | 30 |