What Is the Mode?
The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing data in order to count the frequency of each result. The result with the highest count of occurrences is the mode of the set, also referred to as the modal value.
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 manners. 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 middle, which is also the peak frequency of observed values. For such a distribution, this value is also the mode—the most frequently occurring value in the data.
Other times, the most frequent value may differ from the modal value. For instance, the average frequency of people born with six fingers is something like 0.2%, but the mode is zero since the most common outcome is five fingers.
- 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 Mode
For example, in the following list of numbers, 16 is the mode since it appears more times than any other number in the set:
- 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 2 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 than that.
If no number in a set of numbers occurs more than once, that set has no mode:
- 3, 6, 9, 16, 27, 37, 48
Advantages and Disadvantages of the Mode
Advantages of the mode include:
- It is easy to understand and simple to calculate.
- It is not affected by extremely large or small values.
- It can be located just by inspection in un-grouped data and discrete frequency distribution.
- It can be useful for qualitative data.
- It can be computed in an open-end frequency table.
- It can be located graphically.
Disadvantages of the mode include:
- It is not well defined.
- It is not based on all the values.
- It is stable for large values so it will not be well defined if the data consists of a small number of values.
- It is not capable of further mathematical treatment.
- Sometimes the data has one or more than one mode, and sometimes the data has no mode at all.
When scientists or statisticians talk about the "modal" observation, they are referring to the most common one.