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Unimodal Distribution in Statistics

Probability and Statistics > Descriptive Statistics > Unimodal Distribution

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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 — it refers to the local maximum in a chart. Technically there 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.

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

unimodal distribution

A normal distribution curve, sometimes called a bell curve.

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

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.

Uniform distribution. Image courtesy of the University of Houston.

Image courtesy of the University of Houston.

Bimodal Distribution

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

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.

unimodal

left skewed

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.

Multimodal distribution with many modes, or peaks. Image credit: USDOT

Multimodal distribution with many modes, or peaks. Image credit: USDOT

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.
u dsit

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

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Unimodal Distribution in Statistics was last modified: October 15th, 2017 by Stephanie Glen

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