Bimodal Distribution
A bimodal distribution has two distinct peaks, indicating that data clusters around two different values.
Definition
A bimodal distribution is a dataset with two different peaks or clusters instead of one most-common value, often indicating that the data comes from two different subpopulations that have been combined. It has two distinct local maxima in its frequency or probability distribution, and the overall mean falls between the two peaks, possibly representing neither group well. Formally, a bimodal distribution has two modes, meaning its PDF has two local maxima; mixture models represent this as weighted sums of component distributions, $f(x) = \pi f_1(x) + (1-\pi) f_2(x)$, where $f_1$ and $f_2$ are typically normal PDFs and $\pi$ is the mixing proportion, with parameters estimated via the EM (Expectation-Maximization) algorithm.
Example
Survey scores from a class where half loved the lesson and half disliked it might cluster around $2/10$ and $9/10$, creating two peaks. Heights of a mixed group of adults and children will be bimodal: one peak around adult average heights (5'7") and one around children's heights (4'2"), and the overall mean does not represent either group. A Gaussian mixture model with components $N(\mu_1=3, \sigma_1=1)$ and $N(\mu_2=8, \sigma_2=1.5)$ with mixing weight $\pi=0.4$ has modes at approximately $3$ and $8$, with the EM algorithm iterating between assigning soft memberships and updating parameters until convergence.
Key Insight
Two peaks often mean two different groups are mixed together, so separating and analyzing them individually usually makes more sense than reporting one overall average; bimodal distributions are a sign to look for hidden structure, and clustering algorithms can help identify and separate the two modes. The Hartigan dip test is a formal nonparametric test for unimodality vs. multimodality, and Silverman's bandwidth test uses KDE to test for a single mode, both serving as diagnostic tools before applying mixture models.