### Chapter 1. Descriptive Statistics: Measures of Central Tendency

### Mode

Mode

The **mode **of a distribution is the most frequently occurring score or category.

When looking at a frequency distribution graph, the mode corresponds to the *peak* of the distribution.

Calculating the Mode in Excel

To calculate the *mode* in Excel, make use of the following function:

MODE(array)

array: The array or cell range of numeric values for which you want to calculate the mode.

#\text{Mode} = 2#

The *mode *of a distribution is the score with the highest frequency.

When looking at a histogram, the mode corresponds to the *peak* of the graph.

In this case, the peak of the graph lies at a score of #2#, with an observed frequency of #25#.

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A distinctive characteristic of the mode is that it is a measure of centrality that can be calculated for every type of data. In fact, for nominal data, the mode is the only appropriate measure of central tendency available.

\[

\begin{array}{c|cccc}

&\text{Nominal}&\text{Ordinal}&\text{Interval}&\text{Ratio}\\

\hline

\text{Mode}&\green{\text{Yes}}&\green{\text{Yes}}&\green{\text{Yes}}&\green{\text{Yes}}\\

\end{array}

\]

Sometimes a distribution will have more than one mode. When a distribution has two modes, it is said to be **bimodal**. Strictly speaking, this only occurs when two scores or categories have the exact same highest frequency. In practice, however, the term mode is used more loosely to describe scores with a relatively high frequency.

A bimodal distribution may be indicative of the presence of two distinct subsets within the distribution. Take a look at the histogram below which is the result of measuring the height of #10\,000# Dutch college students. Cleary, this is a distribution with two peaks, one around #171\,\text{cm}# and another around #184\,\text{cm}#. In this case, the first peak corresponds to the female students, whereas the second peak corresponds to the male students.

A distribution with more than two modes is called **multimodal**. It is common practice to not report all the modes of a multimodal distribution since it makes little sense to have three or more *typical* values of a distribution.

If all scores in the distribution occur with the same frequency, the distribution is said to have **no mode**.

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