Mode (statistics)

Definition

In statistics, a mode is a 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. The mode of a set of values is the value(s) that appears most often. It can be used for both numerical and categorical data. The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.

Overview

The mode is one of the basic measures in descriptive statistics. It is considered a measure of central tendency, which is a location parameter that describes a significant point or points in a data set. Other measures of central tendency include the mean and the median. The mode is the least used of the three in general statistical practice, but it is the only measure of central tendency that can be used with nominal data, which have purely qualitative category assignments.

Calculation

The mode is not necessarily unique, since the same maximum frequency may be attained at different values. The definition of mode in mathematical statistics is more precise than in general statistical practice. In particular, a probability density function or probability mass function can have multiple modes, as can the empirical distribution of values in a sample. In the case of discrete (i.e., integer-valued) data, the mode is a value at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

Uses and Importance

The mode is less affected by extreme values than the mean, and is a useful measure of central tendency when the data are categorical or ordinal. The mode is also a common measure of central tendency in many distributions used in the natural and social sciences. It is also useful in distributions that are asymmetrical or have extreme values that would distort the results of the mean or median.

Limitations

The mode is not a robust statistic, meaning that it can be greatly affected by changes in the data. This makes it less reliable as a measure of central tendency, especially for small data sets. The mode is also not defined for data sets that have no repeating values (i.e., each value appears only once).

Multimodal Distributions

In a multimodal distribution, there are two or more modes. This can occur in both discrete and continuous data, and indicates that the data have multiple peaks. This can be an indication of a mixture of two or more underlying distributions.

Mode in Probability Theory

In probability theory, the mode of a continuous probability distribution is the value x at which its probability density function reaches its maximum value, so, informally speaking, the mode is at the peak.