# Mode in math

Here you will learn about the mode in math, including what the mode is and how to find it.

Students will first learn about the mode in math as part of statistics and probability in 6 th grade.

## What is the mode in math?

The mode in math is the most frequently occurring item in a data set. A set of data may have one mode or may be multimodal, meaning it has more than one mode.

A data set with two modes is called bimodal and a data set with three modes is called trimodal. A data set may also have no mode.

For example, find the mode:

The most frequently occurring item is ‘9’ , so 9 is the mode.

For example, find the mode:

The most frequently occurring item is ‘blue’, so ‘blue’ is the mode.

For example, find the mode:

The most frequently occurring items in this data set are ‘1’ and ‘3’ , so 1 and 3 are the modes. This data is bimodal as it has \bf{2} modes.

The mode in math or modal value is a measure of central tendency because it describes a set of numbers by identifying a central position within the data.

## Common Core State Standards

How does this relate to 6 th grade math?

• Grade 6 – Statistics and Probability (6.SP.A.3)
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

## How to find the mode

In order to find the mode:

1. Find the most frequently occurring item.

## Mode in math examples

### Example 1: categorical data

Find the mode of this data set:

1. Find the most frequently occurring item.

You will need to count the number of times the different words occur. The most common item is ‘red’. The number of times ‘red’ occurs is 3 times.

The mode is red.

### Example 2: categorical data

Find the mode of this data set:

Find the most frequently occurring item.

### Example 3: numerical data

Find the mode of this list of numbers:

Find the most frequently occurring item.

### Example 4: numerical data

Find the mode of this list of numbers:

Find the most frequently occurring item.

### Example 5: bimodal

Find the mode of this list of numbers:

Find the most frequently occurring item.

### Example 6: bimodal

Find the mode of this list of numbers:

Find the most frequently occurring item.

### Teaching tips for mode in math

• Provide students with data sets in which the items include various types of numerical values including fractions, decimals, integers, and whole numbers.

• The data sets can also be varied by the number of numbers in the set. Start with data sets that include a low number of values and gradually increase the number of values as well as the complexity of the list of values.

• For struggling students, provide hands-on activities that involve sorting and counting objects rather than worksheets showing only numerical values. For example, provide a basket of colored cubes or counters and have students identify the most frequent color by physically grouping and counting the objects.

• Talk about how outliers can affect the mode. It’s important to note that outliers are less likely to skew the mode than the mean or median. This is because the mode focuses on frequency rather than numerical values or position. However, the presence of extreme outliers can still impact the mode if they occur frequently enough to become the most common value(s) in the data set.

### Easy mistakes to make

• Confusing mode for median or mean
Students hear the terms mean, median, and mode mentioned together frequently in math and can confuse the three terms. Mean is the average value of a data set with numerical values, median is the middle number or middle value when the list of values is placed in ascending order, and mode is the piece of data with the highest frequency within the data set.

• Thinking a data set must have a mode
A data set can have 1 mode or it can be multimodal (have more than 1 mode). But it is possible that a data set has no mode at all.

• Naming the frequency as the mode
The mode will be the item – NOT the frequency.
For example,
Find the mode:
There are 3 As, \, 2 \, Bs , and 6 \, Cs. The item that occurs the most often is ‘C.’ So the mode is ‘C.’ As ‘C’ occurs 6 times, the frequency of C is 6.

### Practice mode in math questions

1. Find the mode:

red

blue

yellow

green

The most common item is ‘yellow’. The number of times ‘yellow’ occurs is 2 times. The other colors only occur once.

2. Find the mode:

Medium

Large

Small

There is no mode

The most common item is ‘small.’ The number of times ‘small’ occurs is 3 times. ‘Medium’ occurs twice and ‘large’ once.

3. Find the mode:

2

3

4

1

The most common item is ‘1.’ The number of times ‘1’ occurs is 2 times. The other numbers only occur once.

4. Find the mode of the following data set:

6

2

2 and 6

There is no mode

The most common item is ‘2’. The number of times ‘2’ occurs is 3 times. The number of times ‘6’ occurs is 2 times, and the other numbers only occur once.

5. Find the mode of this set of numbers:

There is no mode

13

16

12

Each number occurs only one time. Therefore, there is no mode.

6. Find the mode:

10

20

30

10 and 30

The most common items are 10 and 30. They both occur 3 times. This data has two modes. It is bimodal.

7. Theo did a survey of the color of the cars passing his house. The cars were only red, black, silver or blue.

The chart shows the number of red cars, the number of black cars and the number of silver cars. Theo saw a total of 25 cars.

What is the mode of the complete set of data?

red

silver

black

blue

First, you need to find the number of blue cars. To do this, add up the data values of the cars shown on the graph. Then, subtract this number from the total number of cars.

Red – 7
Black – 5
Silver – 9
Total =21

Total number of cars =25

25-21=4. There were 4 blue cars.

This means the color of the car that had the highest frequency was silver, so silver is the mode of the data set.

## Mode in math FAQs

What is the mode in math?

The mode in math is the most frequently occurring item in a data set.

How do you find the mode of a data set?

To find the mode of a data set, look at the entire list of values in the data set and determine which item or number has the highest frequency or occurs most often in the set.

What are descriptive statistics?

Descriptive statistics are used to condense or arrange a collection of data. Arithmetic mean, median, mode, and range are frequently used descriptive statistics to provide an overview of the data set.

How is finding the mode different from finding the median?

Finding the mode is about identifying the value that appears most often in a data set, while finding the median is about determining the middle value in a data set. The mode is about frequency, while the median is about position.

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