A unimodal distribution is a probability distribution with one clear peak.

This is in contrast to a , which has two clear peaks:

This is also in contrast to a , which has two or more peaks:

Note: A bimodal distribution is just a specific type of multimodal distribution.

Examples of Unimodal Distributions

Here are a few examples of unimodal distributions in practice.

Example 1: Birthweight of Babies

It’s well known that the distribution of the weights of newborn babies follows a unimodal distribution with an average around 7.5 lbs. If we create a histogram of baby weights, we’ll see a “peak” at 7.5 lbs with some babies weighing more and some weighing less.

Example 2: ACT Scores

The average ACT score for high school students in the U.S. is about a 21 with some students scoring less and some scoring higher. If we create a histogram of ACT scores for all students in the U.S. we’ll see a single “peak” at 21 with some students scoring higher and some scoring lower.

Example 3: Shoe Sizes

The distribution of men’s shoe sizes is a unimodal distribution with a “peak” around 10. If we create a histogram of all shoe sizes for men, we’ll see a single peak at 10 with some men wearing a larger size and some wearing a smaller size.

Unimodal Distributions in Statistics

The following probability distributions in statistics are all unimodal distributions:

The Normal Distribution

The t-Distribution

The Uniform Distribution

The Cauchy Distribution

Notice that each of these distributions has a single distinct peak.

How to Analyze Unimodal Distributions

We often describe unimodal distributions using three different :

• Mean: The average value
• Median: The middle value
• Mode: The value that occurs most often

Depending on how the distribution is, these three metrics can be in different places.

Left Skewed Distribution: Mean < Median < Mode

In a left skewed distribution, the mean is less than the median.

Right Skewed Distribution: Mode < Median < Mean

In a right skewed distribution, the mean is greater than the median.

No Skew: Mean = Median = Mode

In a symmetrical distribution, the mean, median, and mode are all equal.