# Mode: What It Is in Statistics and How to Calculate It

## What Is the Mode?

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.

### Key Takeaways

• In statistics, the mode is the most commonly observed value in a set of data.
• For the normal distribution, the mode is also the same value as the mean and median.
• In many cases, the modal value will differ from the average value in the data.

## Understanding the Mode

In statistics, data can be distributed in various ways. The most often cited distribution is the classic normal (bell-curve) distribution. In this, and some other distributions, the mean (average) value falls at the midpoint, which is also the peak frequency of observed values.

For such a distribution, the mean, median, and mode are all the same values. This means that this value is the average value, the middle value, and also the mode—the most frequently occurring value in the data.

Mode is most useful as a measure of central tendency when examining categorical data, such as models of cars or flavors of soda, for which a mathematical average median value based on ordering can not be calculated.

## Examples of the Mode

For example, in the following list of numbers, 16 is the mode since it appears more times in the set than any other number:

• 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48

A set of numbers can have more than one mode (this is known as bimodal if there are two modes) if there are multiple numbers that occur with equal frequency, and more times than the others in the set.

• 3, 3, 3, 9, 16, 16, 16, 27, 37, 48

In the above example, both the number 3 and the number 16 are modes as they each occur three times and no other number occurs more often.

If no number in a set of numbers occurs more than once, that set has no mode:

• 3, 6, 9, 16, 27, 37, 48

A set of numbers with two modes is bimodal, a set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

When scientists or statisticians talk about the modal observation, they are referring to the most common observation.

## Mode vs. Mean vs. Median

Mean, median, and mode are all different ways of noting the center of a data set.

Mode is the most common set of numbers, while mean is the average and median is the midpoint.

### Mean

Mean is the average of a set of numbers. To calculate the mean, begin by adding up all of the data points and dividing by the total number of data points. For example, suppose you have the following series of numbers:

• 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48

Added together, you get 208. Divide 208 by 11 (the number of data points) to get the mean, which is 18.9.

### Median

The median is the data point in the middle of a set. To find the median, the numbers in the set must be arranged from smallest to largest. Let's use the numbers in the example above:

• 3, 3, 6, 9, 16, 16, 16, 27, 27, 37, 48

The median is 16, the data point in the exact middle of the set. This set has an odd number of data points, which makes it easier to find the middle. For a set with an even number of data points, you'd take the mean of the two middle numbers to find the median.

• The mode is easy to understand and calculate.

• The mode is not affected by extreme values.

• The mode is easy to identify in a data set and in a discrete frequency distribution.

• The mode is useful for qualitative data.

• The mode can be computed in an open-ended frequency table.

• The mode can be located graphically.

• The mode is not defined when there are no repeats in a data set.

• The mode is not based on all values.

• The mode is unstable when the data consist of a small number of values.

• Sometimes the data has one mode, more than one mode, or no mode at all.

## How Do I Calculate the Mode?

Calculating the mode is fairly straightforward. Place all numbers in a given set in order; this can be from lowest to highest or highest to lowest, and then count how many times each number appears in the set. The one that appears the most is the mode.

## What Is Mode in Statistics With an Example?

The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.

## What Is the Difference Between Mode and Mean?

The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set. The mean is also known as the average.

## The Bottom Line

In statistics, the mode is the number that occurs most often. A data set can have one or more modes. The mode is different from the mean, which is the average of the numbers in a set; it's also different from the median, which is the midpoint of a set. Finding the mode in a set of numbers can tell you which data points occur most commonly, which can be useful information when analyzing statistics.

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