In statistics, one way to describe and analyze data is by using frequency tables.

This lesson will discuss relative and cumulative frequencies and how to calculate percent increase using these two methods.

## Statistics Are on the Rise

When you decide to move to a new home, whether it is in the same city or across the country, one of the first things that you might do is look at the crime statistics for that area. Are they on the rise, or are they declining? You might also look at the schools. How do they stack up against other schools? Are their scores on the way down, or are they rising year after year?All of this information, and information on almost any topic you can think of, can be found using statistics. **Statistics** is the study of the collection and analysis of data.

## Relative and Cumulative Frequency

In mathematics, **frequency** refers to the number of times a particular event occurs. There are two types of frequency: relative and cumulative.

**Cumulative frequency** is the total number of times a specific event occurs within the time frame given. **Relative frequency** is the number of times a specific event occurs divided by the total number of events that occur. Let’s use an example:Your soccer team ended the season with a record of 15 wins and 3 losses.

The cumulative frequency of your wins is 15 because that event occurred 15 times. The relative frequency of wins is 15 divided by 18, or 83%, because, out of the 18 total games (or events), your team won 15.Relative frequency is a good way to predict how often an event might occur in the future. If you know that your soccer team has won 83% of the time in the past, you can reasonably assume that you will win 83% of the time in the future.

## Frequency Table

One of the best ways to tally and organize frequency data is to use a frequency table. A **frequency table** is a table that lists items and shows the number of times they occur.

Below you see an example of a frequency table that describes the different ways students travel to get to school. You can also include a column that gives the relative frequency of each event.

## Percent Increase

Let’s go back to our example of moving to a new town for a minute. If you were to read that the area you wanted to move to had a 2% increase in crime in the last year, you might think twice about moving there.

At the very least, you would do some extra research.What if you discovered in your additional research that the test scores at the local elementary school increased by 23% in the last year? That statistic might be more important to you than the small increase in crime in the same area. The **percent increase** represents the relative change between the old value and the new value. In order to calculate percent increase, you must have collected data about the same event, just at a different time.

## Calculating Percent Increase

To determine the percent increase between two sets of data, you can use a frequency table and the following formula:Percent Increase = Frequency 2 – Frequency 1 / Frequency 1 * 100.Let’s try an example: Data for crime in a certain area was recorded over two years. The following table shows the occurrences of three different types of crime over a two-year period.

And here you see the answers:

The percent increase for eating at home 5 nights a week was 347%, 6 nights a week – 350%, and 7 nights a week – 125%.

## Lesson Summary

Determining the **frequency** and percent increase of events can be very helpful when trying to interpret certain sets of data.

The **cumulative frequency** of a certain event is the number of times that event occurs in a certain time frame. **Relative frequency** refers to the percentage a certain event is of the total amount of events that occur. You can determine the **percent increase** of an event from time to time by using the formula:Percent Increase = Frequency 2 – Frequency 1 / Frequency 1 * 100

## Learning Outcomes

Following this video lesson, you will be able to:

- Explain the usefulness of finding the frequency and percent increase of an event
- Differentiate between cumulative frequency and relative frequency
- Identify the formula for finding percent increase