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A unimodal distribution is a statistical distribution that has one peak or mode. This means that most of the data is concentrated around one specific value and the rest of the data values deviate from that value on either side. An example of a unimodal distribution is a normal distribution, which is shaped like a bell curve and has one peak at the center.
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.