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Math 102: College Mathematics14 chapters | 108 lessons

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

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.

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.

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.

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.

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.

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.

To calculate the percent increase, take each row individually and plug the numbers into the equation.

Percent increase of robbery = ((37 - 33) / 33) * 100 = (4 / 33) * 100 = 0.12 * 100 = 12%

Percent increase of murder = ((8 - 2) / 2) * 100 = (6 / 2) * 100 = 3 * 100 = 300%

Percent increase of assault = ((16 - 15) / 15) * 100 = (1 / 15) * 100 = 0.07 * 100 = 7%

Then, you can complete the table.

Here we have another example: 100 people were asked how often they ate dinner at home in a typical week. Then, they all took a class on how to cook healthy meals at home and after six months were asked again how often they ate at home. What was the percent increase for eating at home 5, 6 and 7 nights a week? Take a minute to try this one on your own.

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%.

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

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

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Math 102: College Mathematics14 chapters | 108 lessons

- Go to Logic

- Go to Sets

- Understanding Bar Graphs and Pie Charts 9:36
- How to Calculate Percent Increase with Relative & Cumulative Frequency Tables 5:47
- Calculating the Standard Deviation 13:05
- Probability of Simple, Compound and Complementary Events 6:55
- Probability of Independent and Dependent Events 12:06
- Either/Or Probability: Overlapping and Non-Overlapping Events 7:05
- Probability of Independent Events: The 'At Least One' Rule 5:27
- How to Calculate Simple Conditional Probabilities 5:10
- Math Combinations: Formula and Example Problems 7:14
- How to Calculate the Probability of Combinations 11:00
- How to Calculate a Permutation 6:58
- How to Calculate the Probability of Permutations 10:06
- Go to Probability and Statistics

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