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

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

This is also in contrast to a multimodal distribution, 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 measures of central tendency:

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

Depending on how skewed 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.

**Additional Resources**

Left Skewed vs. Right Skewed Distributions

Symmetric Distributions: Definition + Examples