  Calculating the Mode

Contributor: Marlene Vogel. Lesson ID: 10136

Have you ever eaten pie a la Mode? That has nothing to do with math, but using different modes of learning and your brain, you will learn about modes! It will be a piece of cake and easy as pie!

categories

Elementary, Middle School

subject
Math
learning style
Visual
personality style
Beaver, Golden Retriever
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Scientists in California want to know the most common magnitude of a series of earthquakes. This information will help them better prepare for any future earthquakes through the use of stronger building materials. What they need to do is take the mode of the scores of the last 10 earthquakes. Not sure how to find the mode of a set of numbers? Come along and let's take a closer look at how to calculate the mode!

Working with numbers helps us figure out information in our lives.

For example, in our opening scenario, scientists are trying to figure out the most common strength of a series of earthquakes. This information will help the scientists work with architects so stronger buildings can be built. The way the scientists can get the answer is to take the Richter scores from the last 10 earthquakes and find the mode among those numbers.

In order to understand how to find the mode in a set of numbers, you first need to define some math vocabulary. On a piece of paper, define the following words. You can look them up in the Merriam-Webster online dictionary or dictionary.com:

• data
• mode
• magnitude
• value

When trying to figure out the mode of a set of numbers, you will first need to put the data (numbers) in order, from the least to the greatest. Let’s use the data from the example problem at the beginning of our lesson.

Scientists in California want to know the most common strength of a series of earthquakes. This information will help them better prepare for future earthquakes through the use of stronger building materials. The last ten earthquakes were measured using the Richter scale, and their magnitudes are listed below. What is the mode of the list of magnitudes?

• 7.0, 6.2, 7.7, 8.0, 6.2, 7.2, 5.4, 6.6, 7.5, 5.9

When you are working with data that is written in the form of decimals, make sure you look at the whole number first (the number to the left of the decimal point). If you have more than one value that begins with the same whole number, then put them in order by looking at the number to the right of the decimal.

At this point, you need to list the numbers from least to greatest, and see if any of the numbers (values) occur more than once.

The number in a set that occurs more than once is the mode.

In our example data, the value 6.2 occurs twice in our list, while every other number occurs only once.

This means that 6.2 is our mode. This is the mode because it is the number that occurs most often in the set of numbers that represent the scores of the last 10 earthquakes.

Is it possible that a set of data can have more than one mode? YES.

If you are working with data and you notice that more than one value (number) occurs more than once, it is possible that there is more than one mode. The important thing in determining if there is more than one mode is that each value that occurs more than one time must appear the same number of times as another value to be an additional mode. Otherwise, the mode will be the value that appears the most times in the set of data.

For example, let’s say we need to find the mode of the following data: 3, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 9.

In that set of data, the numbers 5, 8, and 9 occur more than once. But only the numbers 5 and 8 are the modes because each occurs three times. The number 9 only occurs twice. Remember, the mode is the number in a set of data that occurs the most.

Is it possible that a set of data does not have a mode? YES. It is possible to look at a set of data where each value (number) occurs only once. In that case, the correct answer would be, NO MODE.

The following resource from Math Goodies will help you practice this skill: The Mode of a Set of Data.

Now that you're in mode mode, continue on to the Got It? section to try out your new skill!

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