Bimodal distribution

Bimodal distribution is a probability distribution with two different modes. These appear as distinct peaks (local maxima) in the probability density function. More generally, a distribution with two or more modes is referred to as a multimodal distribution.

Definition

A probability distribution is said to be bimodal if it has two modes. This occurs when the data has two values that appear most frequently. In a histogram representing a bimodal distribution, two areas will have the highest bars.

Examples

A classic example of a bimodal distribution is the height of adult humans. The distribution of heights is bimodal, with one peak representing the average height of men and the other the average height of women. Another example can be found in biology, where a species might have a bimodal distribution of weights or sizes due to differences between males and females.

Properties

A bimodal distribution has several unique properties. It has two modes, but it may or may not have a clear central tendency. The mean, median, and mode can all be different. The distribution can be symmetric or asymmetric, and it can be unimodal or multimodal.

Applications

Bimodal distributions are used in various fields such as statistics, biology, economics, and engineering. They can be used to model phenomena that have two distinct outcomes or states. For example, in quality control, a bimodal distribution might represent a process that is usually in control but occasionally shifts to a state of higher defect rates.

See also

• Probability distribution
• Multimodal distribution
• Mode (statistics)
• Central tendency