What Is the Mode?

The mode is the number that appears most frequently in a set. A set of numbers 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 (mean) 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 not always the case.

Understanding the Mode

In statistics, data are 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, this value is also the modeā€”the most frequently occurring value in the data.

In other distributions, the most frequent value may differ from the modal value. For instance, the average frequency of people born with six fingers is around 0.2%, but the mode is zero since the most common outcome is five fingers.

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 a set of numbers with four or more nodes is multimodal.

Advantages and Disadvantages of the Mode

Advantages:

  • The mode is easy to understand and calculate.
  • The mode is not affected by extreme values.
  • The mode is easy to identify in un-grouped data and 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.

Disadvantages:

  • The mode is not well defined.
  • The mode is not based on all values.
  • The mode is stable for large values and will not be well defined if the data consist of a small number of values.
  • The mode is not capable of further mathematical treatment.
  • Sometimes data have one mode, more than one mode, or no mode at all.

Fast Fact

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