Bimodal Distribution: Definition, Examples & Analysis

A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution. The graph below shows a bimodal distribution.

When the peaks have unequal heights, the higher apex is the major mode, and the lower is the minor mode.

What Causes Bimodal Distributions?

Recognizing that your data follow a bimodal distribution will help you better understand your study topic. This type of distribution usually has an explanation for its existence. Here are several examples.

Merging Two Processes or Populations

In some cases, combining two processes or populations in one dataset will produce a bimodal distribution. Each of the underlying conditions has its own mode. Combine them and, voilà, two modes!

For example, imagine you measure the weights of adult black bears. When you graph the data, you see a distribution with two peaks. It turns out that female black bears have an average weight of 175 pounds while the males average 400 pounds. Each average corresponds to a peak in the distribution. Hence, one peak is for females and the other for males.

Differences between genders frequently produce bimodal distributions.

Or suppose you measure the strength of products from an assembly line and notice a bimodal distribution. After further investigation, you find that one shift uses a slightly different procedure that produces a weaker product. The two processes create dual peaks.

We’ll come back to this example when we analyze an example dataset.

Natural Bimodal Distributions

In other cases, the distribution of the phenomenon you’re studying is naturally bimodal. For example, the size of Weaver ants and the age of onset for Hodgkin’s Lymphoma follow a bimodal distribution. The graph below displays the body lengths of 300 Weaver worker ants from a field study.

In these cases, you can’t separate the bimodal distribution into separate unimodal distributions. However, understanding the bimodal nature will help you better grasp your study area and accurately identify the more common values occurring near the two peaks.

For example, the Weaver ants researcher* hypothesized that the different sized ants had different roles. The smaller variety are caretakers while the larger ones build and defend the nest.

Analyzing Bimodal Distributions

While bimodal distributions occur less frequently, they’re essential to identify when they occur.

Discovering that you’re working with combined populations, conditions, or processes that cause your data to follow a bimodal distribution is a valuable finding. You’ve identified a factor that affects the outcome. You and other scientists can include this variable in future research.

Typically, you’ll want to assess the subpopulations separately to understand their individual distributions better. That process helps you obtain better measures of central tendency and more precise measures of variability for each group. Failure to account for the different distributions can cause unreliable results. For instance, the mean and mode for a bimodal distribution often won’t be near the most common values.

Let’s see this in action!

Example Analysis

Imagine that we gather a random sample from an assembly line and measure the product’s strength. First, we’ll calculate the descriptive statistics for this sample. The results below look relatively straightforward. Here’s the CSV dataset for this example: Bimodal.

Now, let’s graph the data in a histogram.

The statistical summary did not suggest that the data follow a bimodal distribution. Never rely solely on statistical summaries. Always graph your data!

See what else you can learn from histograms.

In the descriptive statistics, notice how the mean and median (both near 60) lie between modes where there are relatively few observations. Typically, these measures find where most values fall, but that’s not the case here, reducing their usefulness in bimodal distributions.

After seeing the histogram, we investigate and find that the shifts use a slightly different procedure. Let’s divide the data by shifts to see the impact of the procedural difference. The histogram below highlights the effect!

Now, let’s calculate the descriptive statistics for each shift.

Notice how the mean and median for groups A and B are roughly 50 and 70 and now fall near the peaks in the histogram above. Also, the standard deviation and range, which are measures of variability, are about half the scale relative to the combined dataset shown earlier. Lower variability means we have a more precise understanding of where the values from each process fall in contrast to the broader bimodal distribution.

Related post: Descriptive Statistics in Excel

Reference

Weber, NA (1946). “Dimorphism in the African Oecophylla worker and an anomaly (Hym.: Formicidae),” Annals of the Entomological Society of America. 39: 7–10.