# Mode

## 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.

The mode can be the same value as the mean and/or median, but this is usually not the case.

## 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 mid-point, which is also the peak frequency of observed values. For such a distribution, the mean, median, and mode are all the same value. This means that this value is the average value, the middle value, 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.

### 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.

## 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.

• 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.