A bimodal graph has two distinct peaks (or humps) separated by a dip in the middle. If you’ve seen a standard bell curve with its single smooth peak, imagine stretching that into a shape more like the letter “M” or a camel’s back. Each peak represents a value where data points cluster most heavily, and the valley between them marks a range where fewer observations fall.
The Key Visual Features
Three elements define a bimodal graph. First, there are two peaks, each representing a “mode,” the most frequently occurring values in that part of the data. Second, there’s a valley or trough between the peaks where the frequency drops. Third, the two peaks don’t have to be the same height. When they’re unequal, the taller one is called the major mode and the shorter one is the minor mode.
Compare this to the two other common shapes. A unimodal distribution has just one peak, like the classic bell curve. A multimodal distribution has three or more peaks. A bimodal graph sits right in between: exactly two peaks, no more, no less. A peak counts anytime the distribution dips and then rises again, even if the second rise doesn’t reach the same height as the first.
Why the Average Can Be Misleading
One of the most important things to understand about bimodal data is that the mean (average) often falls right in the valley between the two peaks, at a value that almost no data points actually represent. The median lands somewhere similar. If you only looked at these summary statistics, you’d think the “typical” value is one that barely exists in your data set. This is why the mode is the preferred summary statistic for bimodal distributions: it points you to where the data actually clusters.
Imagine measuring the commute times of employees at a company with two office locations, one 15 minutes away and one 45 minutes away. The average commute might be 30 minutes, but very few employees actually have a 30-minute commute. The bimodal graph would show you the real story: two humps at 15 and 45 minutes with a dip in between.
The Classic Example: Human Height
The most famous bimodal distribution in statistics textbooks is the combined height of men and women. If you plot the heights of a mixed group of adults on a single graph, you’ll typically see one peak near the average female height and another near the average male height. U.S. survey data for adults aged 20 to 29 shows men averaging about 69.3 inches (5’9″) and women averaging about 64.1 inches (5’4″), with standard deviations of roughly 2.9 and 2.75 inches respectively.
A histogram of college students’ heights, for instance, would show a cluster around 5’5″ to 5’6″ for women and another around 5’10” to 6’0″ for men. The valley in between, around 5’7″ to 5’8″, would have noticeably fewer people. Separate each group by sex, and each one becomes a standard unimodal bell curve. This points to a broader pattern: bimodal graphs often appear when your data combines two distinct subgroups.
Everyday Examples of Bimodal Patterns
Bimodal distributions show up in daily life more than you might expect. Restaurant foot traffic follows a bimodal pattern throughout the day, with one surge around lunchtime and another during the dinner rush between 6 and 8 pm. The hours between those peaks see far fewer customers, creating that signature two-humped shape when you plot traffic volume against time of day. Restaurants actually use this pattern strategically, offering steeper discounts during slow periods (as high as 34% at 4 pm) compared to peak dinner hours (around 15% at 7 pm).
Other real-world examples include the distribution of eruption intervals at Old Faithful (which alternates between shorter and longer wait times), the times people commute to and from work (morning and evening rush hours), and test scores in a class where one group studied and another didn’t.
How Bin Size Affects What You See
If you’re creating a histogram from your own data, the width of the bins (the bars in the chart) can hide or reveal bimodality. Bins that are too narrow create a jagged, noisy graph with random spikes that make it hard to see any overall pattern. Bins that are too wide smooth everything out into what looks like a single broad hump, completely obscuring the two-peaked structure.
The sweet spot follows standard rules like the Rice rule, which calculates an appropriate number of bins based on your sample size. In one example using blood pressure data, narrow bins produced visual noise, wide bins hid the bimodal shape entirely, and a balanced bin width clearly revealed two peaks at about 70 mm Hg and 110 mm Hg. If you suspect your data might be bimodal but your histogram looks unimodal, try adjusting the bin width before drawing conclusions.
How to Confirm Bimodality Statistically
Eyeballing a graph isn’t always reliable, especially with small data sets or noisy data. One formal approach uses the bimodality coefficient, a single number between 0 and 1 calculated from the skewness and kurtosis of your data. Values greater than 5/9 (about 0.556) suggest a bimodal distribution, while values below that threshold point toward a unimodal one. A score of 1 represents the most extreme bimodal case, where data clusters entirely at two distinct values with nothing in between.
This coefficient is useful as a quick check, but it’s not foolproof. Heavily skewed unimodal distributions can sometimes produce coefficients above the threshold, so it works best as a screening tool alongside visual inspection. If your histogram shows two peaks and the bimodality coefficient confirms it, you can be fairly confident you’re dealing with genuinely bimodal data rather than random variation.