Everything about Bimodal Distribution totally explained
In
statistics, a
bimodal distribution is a
continuous probability distribution with two different
modes. These appear as distinct peaks (local maxima) in the
probability density function, as shown in Figure 1.
A good example is the height of a person. The heights of males form a roughly
normal distribution, as do those of females. Each of these distributions is unimodal. However, if we plot a single histogram of the entire population, we see two peaks—one for males and one for females.
Bimodality is a property of many distributions. A bimodal distribution most commonly arises as a mixture of two different
unimodal distributions. In other words, the bimodally distributed random variable X is defined as
with probability
or
with probability
, where
Y and
Z are unimodal random variables and
is a mixture coefficient. In the height example,
Y would be the height of a random male,
Z the height of a random female, and
the probability that a random individual is male.
Bimodal distributions are a commonly-used example of how summary statistics such as the
mean,
median, and
standard deviation can be deceptive when used on an arbitrary distribution. For example, in the distribution in Figure 1, the mean and median would be about zero, even though zero isn't a typical value. The standard deviation is also very large, even though the deviation of each normal distribution is relatively small.
More generally, a
multimodal distribution is a continuous probability distribution with two or more modes, as illustrated in Figure 2. A
unimodal distribution has only one mode.
Further Information
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