Cumulative relative frequency refers to the proportion of data values that are less than or equal to a certain value. It is usually expressed in the form of a percentage.

For example, suppose that in a test of 100 marks the cumulative frequency for 60 marks is 85%. This means that 85% of the students have obtained less than 60 marks in the exam.

The cumulative relative frequency can be represented easily in the form of a cumulative relative frequency table.

**How do you find the cumulative relative frequency?**

- Represent the data in the form of a frequency distribution table.
- Find the cumulative frequencies by summing up the frequencies of the current and the preceding class intervals.
- Divide the cumulative frequencies by the total frequency. This gives us the cumulative relative frequency.
- If needed, we convert the cumulative relative frequencies obtained above into percentages by multiplying the proportion by 100.

**Example**:

Consider the following data given in the form of a frequency table.

Class Intervals | Frequency |

0-10 | 10 |

10-20 | 15 |

20-30 | 7 |

30-40 | 18 |

We find out the cumulative relative frequency table as follows.

*Step 1*: We find out the cumulative frequency by adding up the frequencies of the current and previous class intervals.

Class Intervals | Frequency | Cumulative Frequency |

0-10 | 10 | 10 |

10-20 | 15 | 10+15 = 25 |

20-30 | 7 | 10+15+7 = 32 |

30-40 | 18 | 10+15+7+18 = 50 |

TOTAL = 50 |

*Step *2: We find out the relative cumulative frequency by dividing the cumulative frequency by the total frequency.

Class Intervals | Frequency | Cumulative Frequency | Relative Cumulative Frequency |

0-10 | 10 | 10 | 10/50 = 0.2 |

10-20 | 15 | 25 | 25/50 = 0.5 |

20-30 | 7 | 32 | 32/50 = 0.64 |

30-40 | 18 | 50 | 50/50 = 1 |

Total=50 |

*Step *3: We convert the relative cumulative frequency into percentages by multiplying it by 100

Class Intervals | Frequency | Cumulative Frequency | Relative Cumulative Frequency |

0-10 | 10 | 10 | 0.2 or 20% |

10-20 | 15 | 25 | 0.5 or 50% |

20-30 | 7 | 32 | 0.64 or 64% |

30-40 | 18 | 50 | 1 or 100% |

Total=50 |

**Remarks**:

1. The cumulative relative frequency for the last class must always be 1 because we are dividing the total frequency by itself to calculate the final cumulative relative frequency.

2. A cumulative relative frequency distribution shows us the percentage of data values that lie below an upper class interval.

3. A cumulative relative frequency graph or a cumulative frequency histogram is drawn in the usual way except for the fact that we plot the cumulative relative frequencies on the Y axis.