The mode is one of the ways to express the average of a set of data. This lesson will define mode and give some real life examples of how it is used in statistics. There will be a quiz at the end to solidify the concepts.

## Statistics

In statistics, there are three common ways to find the average of a group of data. They are the mean, the median and the mode.

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Statisticians choose which calculation of the average to use based on the type of data they are studying. Here is a brief overview of the three:

1. Mean: this is the calculation that is most often thought of when talking about average. It is calculated by adding up all the numbers in a data set and then dividing that sum by the total of numbers that are being added.
2. Median: the median is the middle number of a set of data. This type of average is used most often when talking about income or property values, since it will discount any effects from outliers, numbers that might be way off from the rest of the group.
3. Mode: the mode is the number that occurs most often in a set of data.

## Sample Problems

As stated above, the mode is the number in a group that occurs most often.

Lets go through some examples.

#### Example 1

What is the mode of this group of numbers?2, 2, 4, 6, 3, 4, 2, 5, 8Since there are three 2s, 2 is the mode of this set.A group of numbers can have more than one mode, or there can be none at all.

Look at a couple of other examples.

#### Example 2

Find the mode:5, 6, 2, 5, 8, 7, 4, 9, 1, 4This set of numbers has 2 modes, 4 and 5; these numbers both occur twice, while all the other numbers occur only once.

#### Example 3

Find the mode:7, 3, 8, 11, 5, 19, 4, 10This group does not have a mode, because all the numbers occur only once.

## Methods for Finding the Mode

It might seem easy just to look at a group of numbers and pick which one occurs most often, but that can lead to confusion and incorrect answers. There are two methods that can help you organize the group in order to find the mode.First, you can look at a group of numbers and cross out those that aren’t a possibility.

Start with the numbers that occur only once and cross them out. Then find the numbers that occur twice and cross them out. Finally, you will be left with the numbers that occur most often, and it can be easier to pick identify the mode or modes.Second, and probably the most organized way, is to rearrange the numbers in order from smallest to largest.

Then you will have a better grasp of which one occurs most often. Take, for example, this set of numbers:2, 7, 4, 7, 8, 17, 5, 9, 10, 4, 7, 12, 3Rearrange the set to look like this:2, 3, 4, 4, 5, 7, 7, 7, 8, 9, 10, 12, 17Arranging the numbers in order makes it easy to see that 7 is the mode, because it occurs most often.

## When Is Mode Most Useful?

The mode form of average is most often used when determining opinions and trends. If you give a group of people five books to read, and they each pick their favorite, the most popular book will be the one chosen most often. The same can be true with breakfast cereal, fashion, leaders. .

. almost anything. Let’s look at some examples.A group of people, in a blind taste test, are asked to pick which soda they prefer.

The cups are numbered 1-5, and the answers are:1, 3, 2, 4, 2, 5, 3, 4, 1, 1, 3, 2, 1, 1, 4, 5, 1, 3, 5, 2Which choice represents the mode and is therefore the most popular? For this question it will be best to arrange the data in numerical order to determine the mode1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5This arrangement makes it easier to see that the answer is 1.

## Lesson Summary

The mode is one of the statistical means for finding the average of a group of numbers. The mode of a set of data is the number that occurs most often. A group can have more than one mode, or there can be no mode. It is useful when determining the preferences of a group.