A bimodal distribution most commonly arises as a mixture of two different unimodal distributions (i.e. distributions having only one mode). In other words, the bimodally distributed random variable X is defined as Y with probability α or Z with probability (1 − α), where Y and Z are unimodal random variables and 0 < α <> is a mixture coefficient. For example, the bimodal distribution of sizes of weaver ant workers shown in Figure 2 arises due to existence of two distinct classes of workers, namely major workers and minor workers[1]. In this case, Y would be the size a random major worker, Z the size of a random minor worker, and α the proportion of worker weaver ants that are major workers.
A mixture of two unimodal distributions with differing means is not necessarily bimodal, however. The combined distribution of heights of men and women is sometimes used as an example of a bimodal distribution, but in fact the difference in mean heights of men and women is too small relative to their standard deviations to produce bimodality[2]. A mixture of two normal distributions with equal standard deviations is bimodal only if their means differ by at least twice the common standard deviation[2].
