## Finding the mode (most frequently observed value) in a set of numbers provides a practical method to summarize data into a typical value or statistic.

What is a mode?

The modal value is the the score or value that occurs most frequently in a set of numbers. To find the mode, we count how many times each value is observed and place the results into a frequency distribution. The most frequently observed value or values is the mode.

How do I calculate a modal value?

In order to find the mode, we list the values in the data set by how frequently each one is observed. For example, in the data set {1, 2, 3, 4, 4, 5}; the values 1, 2, 3, and 5 each occur once:

1 - X

2 - X

3 - X

4 - XX

5 - X

4 is observed twice, so the modal value is 4.

When more than one score is observed with highest frequency, the data set may be bimodal (two modes) or multimodal (more than two modes). In the data set {12, 13, 13, 14, 15, 15}, there are two modes of 13 and 15 and the distribution can be described as bimodal. If there are no repeated values in a data set, no modes exist.

Why is it important to know the modal value?

The mode is a measure of central tendency. It is a summary statistic that provides us with a description of the most frequently observed value in a data set.

What do I need to know about the mode?

The mode is very useful with nominal and ordinal data or when the data is not normally distributed. For example, if a company is trying to determine which of 5 soft drinks to promote, the marketing department might survey a group of consumers to determine which beverage consumers prefer. In a sample of fifteen consumers who were asked to list their favorite soft drink, the following results were reported:

Brand A: XXXX

Brand B: XXXXXXXXX

Brand C: XX

Here, Brand B was listed 9 times as the favorite drink. The modal value is Brand B.

The mode is not affected by extreme values or outliers. This means that in skewed distributions (where there are extreme values at one end of the distribution), the mode is a good summary statistic.