Descriptive Statistics > Unimodal Distribution

## Unimodal Distribution : Overview

A unimodal distribution is a distribution with **one clear peak** or most frequent value. The values increase at first, rising to a single peak where they then decrease. The “mode” in “unimodal” doesn’t refer to the most frequent number in a data set (although it’s closely related)—it refers to the local maximum in a chart. Technically they are the same thing: one mode (one common number) will equal one peak in a graph. However, when you are looking at a graph and trying to decide if it’s a unimodal distribution or not, there’s no list of numbers to guide you.

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The normal distribution is an example of a unimodal distribution; The normal curve has one local maximum (peak).

Other types of distributions in statistics that have unimodal distributions are:

- The uniform distribution.
- The T-distribution.
- The chi-square distribution.
- The Cauchy distribution.

In elementary statistics, you probably will see the first three types of distribution listed above, but not the Cauchy. The Cauchy is a particular type of distribution where the expected value does not exist. See here for more information on the Cauchy distribution.

The **uniform distribution **is a type of probability distribution where the odds of getting any number within the range are the same. For example, if you roll a die, your odds of rolling any number (1, 2, 3, 4, 5, 6) are the same.

### Bimodal Distribution

“Bi” means two, so there are *two* local maximums (peaks) in a bimodal distribution.

### Symmetry and the Unimodal Distribution

Unimodal distributions aren’t necessarily symmetric like the normal distribution. They can be asymmetric, or they could be a skewed distribution.

## Other types of distributions

**Multimodal distributions**, where there are more than two peaks, are very rare. One example of a multimodal distribution is a** trimodal** distribution, which has three peaks.

**U distributions** have a distribution in the shape of the letter U, with large frequencies at the left and right of the distribution and few values in the middle.

**Fun fact**: The mean, median and mode often occur in alphabetical order (or reverse alphabetical order) on unimodal distributions.

## References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. SAGE.

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