**The accumulated frequency is the result of successively adding the absolute or relative frequencies, from the smallest to the highest of their values.**

To calculate the cumulative frequency, the data must be sorted from lowest to highest. For a simpler calculation and a more visual image, these are placed in a table. After having the data ordered and tabulated, the accumulated frequency is obtained simply by adding a class or group of the sample with the previous one (first group + second group, first group + second group + third group and so on until accumulating of the first group to last).

**Types of accumulated frequencies**

There are two types of cumulative frequency, the absolute and the relative:

**1. Accumulated absolute frequency**

Absolute frequency gives us information about the number of times an event is repeated when performing a certain number of randomized experiments. To find the accumulated absolute frequency, we would have only to accumulate the absolute frequencies. This is called with the letters Fi.

Assume that the grades of 20 students in the first year of economics are the following:

1,2,8,5,8,3,8,5,6,10,5,7,9,4,10,2,7,6,5,10.

To find the absolute cumulative frequency, the data is first sorted from lowest to highest, tabulated and then accumulated.

Therefore we have:

Xi = Statistical random variable, note of the first economics course exam.

N = 20

fi = Number of times the event is repeated (in this case, the exam grade).

Xi |
fi |
Fi |

one | one | one |

two | two | 3 |

3 | one | 4 |

4 | one | 5 |

5 | 4 | 9 |

6 | two | eleven |

7 | two | 13 |

8 | 3 | 16 |

9 | one | 17 |

10 | 3 | twenty |

∑ | twenty |

** **

To emphasize is that the total of accumulating the absolute frequencies, has to coincide with the total of the sample. This is a good way to verify that it has been calculated correctly.

**2. Cumulative relative frequency**

The relative frequency is calculated as the ratio of the absolute frequency of some value of the population / sample (fi) among the total values that make up the population / sample (N). To find the cumulative relative frequency, we would only have to accumulate the relative frequencies. This is called with the letters Hi.

Assume that the grades of 20 students in the first year of economics are the following:

1,2,8,5,8,3,8,5,6,10,5,7,9,4,10,2,7,6,5,10.

Therefore we have:

Xi = Statistical random variable, note of the first economics course exam.

N = 20

fi = Number of times the event is repeated (in this case, the exam grade).

Hi = Proportion that represents the ith value in the sample.

Xi |
fi |
hi |
Hi |

one | one | 5% | 5% |

two | two | 10% | fifteen% |

3 | one | 5% | twenty% |

4 | one | 5% | 25% |

5 | 4 | twenty% | Four. Five% |

6 | two | 10% | 55% |

7 | two | 10% | 65% |

8 | 3 | fifteen% | 80% |

9 | one | 5% | 85% |

10 | 3 | fifteen% | 100% |