< List of probability distributions

A **relative frequency distribution** expresses the frequency distribution of a variable in percentages or proportions, either on a table or graph. In other words, it shows how often an event happens, compared to other events. This is useful for observing and comparing the frequencies of different values or classes of values.

For example, comparing the frequency of different weather events can be done with a relative frequency distribution.

## How to create a relative frequency distribution

First, to create a relative frequency distribution, we need to calculate the frequency of each value or class. The *frequency *refers to the number of observations that are within each category. The following table shows a frequency distribution with counts (“frequency”) showing how often an adverse weather event happens in a certain city in a calendar year:

After calculating the frequencies, we can then compute the relative frequencies by dividing each frequency by the total number of observations. Percentages and proportions are two ways to express relative frequencies. Percentages are denoted as numbers out of 100, whereas proportions are denoted as numbers out of 1. The following relative frequency distribution shows the same information on adverse weather events, except that this time there is a third “relative frequency” column. These are calculated as follows:

- Count the total number of items. In this table the total is 67.
- Divide the count (the frequency) by the total number of items. For example, hurricanes were seen 12 times, divided by the total (67) gives 12/67 = 0.179.
- Sum up the relative frequencies to get the total. This should equal 1 in decimal or 100% in percentages.

One way to visualize a data distribution is using a *frequency distribution histogram*. This displays the relative frequency of each event on the y-axis.

## Why use a relative frequency distribution?

Relative frequency distributions are an important tool for understanding the distribution of a variable. They can be used to compare the frequencies of different values or classes of values, and to answer a variety of questions, such as:

- What is the most common type of adverse weather event?
*From the graph above, that’s rain*,*which has the tallest bar.* - What percentage of events are hurricanes?
*From the above table, hurricanes happen at a relative frequency of 0.179 or 17.9%.* - What percentage of adverse weather events happen less than 10 times per year?
*From the above table, only one event happens less than 10 times per year: snow.*

Use relative frequency distributions when you need to quickly and efficiently analyze the trends of a data set.

## Cumulative Relative Frequency

To obtain the cumulative relative frequency, follow the above-mentioned steps to generate a relative frequency distribution table. Then, in an additional column labeled “cumulative relative frequency,” add up the relative frequencies as you go down the column.

- The first entry in the column is the same as the first entry in the relative frequency column (.179).
- Add the first and second entries to get 0.179 + 0.224 = 0.403.
- Add the first, second and third entries to get 0.179 + 0.224 + 0.433 = 0.836.
- Add the first, second, third and fourth entries to get 0.179 + 0.224 + 0.433 + 0.15 = .851.
- Add the first, second, third, fourth and fifth entries to get 0.179 + 0.224 + 0.433 + 0.15 + .149 = 1.00.