# Bimodal Distribution

< Probability distribution list < Bimodal distribution

A bimodal distribution has two modes that may or may not be symmetric [2].

Most probability distributions has one peak, which happens around the mean or median [3]. For example, a bell curve typically shows concentration of observations, typically around the mean. However, a bimodal distribution has two distinct peaks – showing that data points are distributed across two separate values.

A mode indicates there is a single most common number within a set of data points, the “mode” in a bimodal distribution identifies two local maximums — where values stop trending up and start trending down. The mean and median lie between the two peaks and are not near either one [3].

The “bi” in bimodal distribution comes from the Latin bis, which means two. “Modal” refers to the peaks.

## What a Bimodal Distribution tells you

• Two peaks may indicate two different groups [2]. For example:
• Exam scores often have a single peak, indicating that students are of similar ability. However, bimodal distributions can appear in grades sometimes – with many getting As and Fs – which suggests two distinct groups at play. This may be evidence of one group being more prepared than the other: either due to a lack or surplus of prior knowledge.
• A bimodal distribution might result from a natural process such as the breakup of large particles, multiple sources of particles or variable growth mechanisms in a system [4]. In climatology, the Lifetime Maximum Intensity (LMI) distribution of tropical cyclones (defined as the peak one-minute maximum sustained wind achieved by a tropical cyclone during its lifetime) is bimodal, which means that major storms are not very rare compared to less intense storms [6] — although there is no consensus on why this bimodality occurs. [7].
• Two peaks could also indicate your data is sinusoidal (wave-like). If you suspect your data might be following a wave-like pattern, create a scatter or run sequence plot to double-check for sinusoidal patterns. If the data points form a wave-like pattern, this would be a strong indication that the data is sinusoidal. If data is smooth with regular frequency and is symmetrical, that also indicates a sinusoidal pattern:
• Peaks and troughs occur at regular intervals.
• Peaks and troughs are of equal height (i.e., symmetrical).
• Data is smooth, with no sudden jumps or changes in the data.
• Sometimes, what looks like a bimodal distribution might be two unimodal distributions. For example, this following image shows two separate distributions graphed on the same axes.

A mixture of two normal distributions will not be bimodal unless there is a large difference between their means — typically bigger than the sum of the individual distribution’s standard deviations [5].

## References

[1] Qwfp at English Wikipedia, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons

[5] Schilling, M. et al. (2002). Is Human Height Bimodal? The American Statistician, Vol. 56, No. 3, (Aug., 2002), pp. 223-229

[6] Lee, C. et al. (2015) Rapid intensification and the bimodal distribution of tropical cyclone intensity. Nature Communications. DOI: 10.1038/ncomms10625

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