### 3.9: What is a Mode?

The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.

There can be more than one mode in a data set if multiple values have the same highest frequency. For instance, suppose that the Statistics exam scores of 20 students are: 50; 53; 59; 59; 63; 63; 72; 72; 72; 72; 72; 76; 78; 81; 83; 84; 84; 84; 90; 93. Here, the mode is 72, as it occurs most frequently, five times.

A data set with two modes is called bimodal. For example, if five students score the following marks in a test, 430, 430, 480, 480, 495, then the data set is said to be bimodal because the scores 430 and 480 occur twice each. A dataset can be multimodal or have no mode.

The mode can also be used for qualitative data. Consider a box with three red, two green, one yellow, and two purple balls. Since red balls occur with the highest frequency, red is considered as mode. Moreover, the mode is the only measure of central tendency that can be used for any data measured on a nominal scale, such as surveys and pie charts.

However, its use in statistical analysis is limited because it is not algebraically defined and requires calculating the frequency of the elements in a data set. Moreover, data sets with small sample sizes can have fluctuations in the frequency of some of these data, making it difficult to ascertain the central tendency of the data set via its mode.