- [Arithmetric Mean]?
- [Normal Distribution]?
- [Standard Deviation]?
In statistics, a bimodal distribution is a distribution with two different peaks -- that is, there are two distinct values that measurements tend to center around. Unlike other distributions such as the normal distribution, there is no precise definition of a bimodal distribution. A good example is the height of a person; the heights of males form a roughly normal distribution, as do those of females, but when added together we obtain a bimodal distribution with values clustering around both the averages.
As in this example, observing a bimodal distribution typically indicates that the distribution is in fact the sum of two different distributions, each with a single notable peak. However, it can be difficult to find the differentiating factor between those samples in one distribution and those in the other.
Bimodal distributions are a commonly-used example of how deceptive summary statistics such as the mean, median, and standard deviation can be when used on an arbitrary distribution. For example, in the distribution in Figure 1, the mean and median would be about zero, but most values are not concentrated near zero. The standard deviation is also very large, even though the deviation of each normal distribution is relatively small.
Figure 1. A simple bimodal distribution, in this case the sum of two normal distributions