# What is the Mode?

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Definition:

A mode is a type of mathematical average which finds the most common or frequently occurring number in a set of data.

## 🤔 Understanding mode

The mode of a dataset is the most common number in that set of data. It’s one of a few different types of mathematical averages or central tendencies, such as a median and mean. When you look at a set of data, various information, such as the middle point of data or the most common result can be valuable for different types of analysis. When the same number can happen in a set of data more than once, finding the mode means finding the one that occurs the most often.

Example

A teacher gives an exam to a class of 10 students, the exam includes 20 questions, and the students receive the following scores.

• 1
• 2
• 15
• 15
• 15
• 15
• 16
• 16
• 18
• 20

The mode of the test scores is 15, because it is the most common score among students. This differs from the mean (sum of scores divided by number of scores), 13.3, but in this case is the same as the median (number that falls in the middle of a range of values).

## Takeaway

A mode is like a popularity contest…

When you take a survey to find the most popular type of pet, you count up the number of responses for each pet. You want to know that 15 people prefer dogs and 23 prefer cats, making cats the most popular choice. Finding a mode is similar to taking a survey because you want to know the most common result in a dataset rather than something like the median or mean result.

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## What is the mode?

The mode of a set of data is the most frequently occurring number within that dataset. It is a type of mathematical average, like a median or mean, that statisticians use when analyzing data.

Any set of data can have multiple modes, if more than one result ties for being the most common — Or there can be no mode, if every number appears only once. An example of where the mode is useful is when taking a survey. For example, you ask everyone in a group to name pizza toppings that they enjoy. One person might name pepperoni and peppers, and the second might name pepperoni and ham, and the third might only enjoy cheese.

The most common preference is pepperoni. The person placing the order can use that information when deciding what to purchase.

Looking at the mode of a set of data can also reduce the impact of outliers. Consider a town of 100 families. One family makes \$10M per year while the other families each earn \$50,000 per year.

The mean (aka average) income in the town is \$149,500, but the mode income is \$50,000 per year. Someone considering only the mean would believe that the town’s residents tend to make far more than they really do.

## What is the difference between mean, median, and mode?

Mean, median, and mode are all different types of mathematical averages. The mean of a set of data is the sum of each data point divided by the number of data points. It’s what people most commonly think of when they hear the word average.

For example, in the following data set:

• 10
• 10
• 10
• 12
• 15
• 18
• 20

The mean is 15.57.

The formula for finding the mean is:

Sum of data points / Number of data points = mean

The median is the middle point of data in a group of data points. To find the median, order the data points from largest to smallest or smallest to largest, then find the point that falls in the middle. If there are an even number of data points, add the two middle data points, and then divide by two. In the dataset used above, the median is 12.

The mode is the most common data point in a set of data points. In the above example, the mode is 10, because it appears three times, while no other result appears more than once.

## How do you find the mode if there are two?

A dataset may have any number of modes. There may be no mode, one mode, or more than one mode.

If every result appears in a dataset the same number of times, then there’s no mode in that set of data. For example, the following dataset has no mode:

• 1
• 2
• 3
• 4

If two different results tie for the most appearances in a dataset, then both of those results are the mode. When this happens, the dataset is bimodal. In the following example, both 2 and 4 are the modes because they appear twice each while other results only appear once.

• 1
• 2
• 2
• 3
• 4
• 4
• 5

A dataset can also have three (trimodal), four (quadrimodal), or any number of modes (multimodal) — if, like in the example above, multiple results tie for the most appearances in the dataset.

## What is the mode used for?

The mode is useful when you want to find the most common number that shows up in a set of data. Depending on your goals, finding the mean, median, or the mode may provide useful information.

Modes are particularly useful when talking about things like survey results rather than numerical data, such as test scores.

For example, a school district creating a budget might take a survey of students and parents in the district to learn about the most popular programs. Finding the mode response to the survey will show the school district the most popular program. That can guide the decision-makers away from cutting that program.

A state government might collect data on how people commute to work each day. If the most common answer is car, the government might decide to invest in road infrastructure. If more people answer with public transportation, the government might increase the budget for subways and buses.

## When should the mode be used?

Compared to the median and mean, the mode isn’t used often when summarizing or analyzing many types of data.

Modes are used when you primarily want to find the number that shows up most often in a dataset. For example, if you want to know the most frequently occurring winning score in a football game, you could use a mode.

Another time modes are useful is when there’s a relatively finite number of potential results in the dataset compared to the number of data points. If thousands of students took an exam with scores ranging from 0 to 100, then the mode may be a useful measure.

Modes are particularly useful when looking at categorical data. Categorical data is any kind of data that you can divide into groups. For example, level of education is categorical data because you can divide it into groups, such as:

• Did not graduate high school
• High school graduate or GED
• Some college
• Associate’s degree
• Bachelor’s degree
• Master’s degree
• PhD.

The mean and median don’t provide much information or make sense when considering categorical data, but the mode can tell you the most common category.

## When should the mode not be used?

Mode should not be used when there’s a large number of possible results in a dataset, especially compared to the number of data points in the set. Finding the mode height of a basketball team that includes a dozen players is less useful than finding the mean or median height. Any duplication of heights in such a small sample is likely coincidental whereas the mean or median height is useful for comparing to other teams.

For another example, a mode will be more useful for a test on a scale from one to 10 when there are 1,000 test takers than a test on a scale from one to 1,000 with 1,000 test takers.

In the world of finance, modes are not frequently used for technical analysis or stock analysis. For example, analysts might look for the standard deviation from the variance in a fund’s returns or the standard deviation from its mean returns. They would not be likely to look for the mode.

Statisticians also would not be likely to run a t-test to compare the modes of two datasets. They would use the test to compare the dataset’s means or medians. Modes are also ill-suited for use with small datasets. It can be more difficult to find a mode when there are only a few numbers in a set of numbers. They, like means, can also change frequently as additional numbers are added to the set.

One advantage of finding the mode of a dataset is that it’s relatively easy to do. Look at the results in a dataset and find the most common one. Another advantage of mode is that it’s useful for working with non-numerical data. For example, if you can break a dataset into categories, such as age group, level of education, or hair color, you can use the mode to find the most frequent occurrence.

A drawback of a mode is that it has limited mathematical usefulness when compared to a median or a mean. For example, when a dataset is open-ended, such as looking at people’s heights, a mode isn’t very useful. There is almost no limit to the different heights people can have, especially if you measure down to tenths or hundredths of a centimeter.

For an example of why mode is less useful than median or mean in these situations, consider a clothes maker who is designing shirts for a school’s field day. Knowing the mean or the median height of each class can help that clothes maker decide on how many shirts of each size to make. If the clothes maker had the mode height instead, they wouldn’t be able to make sizing decisions as easily because it might just be luck that a class had two equally and unusually tall or short students. In many cases, there would be no mode at all, providing the clothes maker with no guidance.

Another drawback of modes is that datasets don’t always have a single mode. With median and mean, you can calculate and know the one median or mean of a dataset. With modes, there can be any number of modes or none at all.

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