# Frequency distribution

The frequency distribution is the way in which a set of data is classified into different mutually exclusive groups. That is, if a piece of data belongs to one group, it cannot belong to another.

The frequency distribution, in other words, is the way in which a series of observations is arranged in different groups, and usually in an ascending or descending way.

To see it in an example, a group of people can be grouped according to their age in ranges of 18 to 25 years, 26 to 40 years, 41 to 60 years and 61 years and over.

It should be noted that the frequency distribution is usually made with respect to a statistical sample, although it could also be based on an entire population.

Another aspect to take into account is that the groups in which the data are distributed can be specific numbers, for example, if the variable is the number of times the person has taken an evaluation, which can be 1, 2 or 3. Although, as we saw lines above, it may also be that you are working with intervals.

## Types of frequency distributions

The types of frequency distributions are as follows:

- Absolute frequency (fi): It is the number of observations that belong to each group. Also, it is interpreted as the number of times an event is repeated.For example, continuing with the previous case, it may be that of a group of 100 people, 20 of them are between 26 and 40 years old.
- Relative frequency (hi): It is calculated by dividing the absolute frequency by the number of data, for example, returning to the situation outlined above, 20/100 is equal to 0.2 or 20%.
- Cumulative absolute frequency (Fi): It results from adding the absolute frequencies of a class or group of the sample (or population) with the previous one or the previous ones. For example, to calculate the cumulative absolute frequency of the third group, the absolute frequencies of the first, second and third groups are added.
- Accumulated relative frequency (Hi): It is the result of adding the relative frequencies, as explained for the accumulated absolute frequency. For example, to calculate the cumulative relative frequency of the fourth group, the relative frequencies of the first, second, third, and fourth groups are added together.

## Example of frequency distribution

Let's see an example of a frequency distribution table:

fi | hi | Fi | Hi | |
---|---|---|---|---|

[18-25] | 35 | 0,35 | 35 | 0,35 |

[26-40] | 20 | 0,2 | 55 | 0,55 |

[41-60] | 27 | 0,27 | 82 | 0,82 |

60 or more | 18 | 0,18 | 100 | 1 |

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