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Bimodal Distribution

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Statistics is the study of data. It deals with collection, interpretation, organization and analysis of data. Mean, median, and mode are three important  terms of statistical studies. Mean is the average of all the numbers in a given data set. Median is the middle number when all the numbers of the data set are written in an order. Mode is the most repeated number of the data set.
A distribution of a variable is the pictorial description of how many times a possible outcome will come in a certain number of trials. We can make a distribution for how many times head will come if a coin is flipped four times. A frequency distribution gives the description of how often one value occurs in a data set.

A frequency distribution chart can been categorized on the basis of the number of modes it has:

1) Unimodal distribution:  It has only one mode.

2) Bimodal distribution: It has got two modes.

3) Multi-modal distribution:   It has got more than two modes.

Definition

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Bimodal distribution defines a data set having two modes, that is, when a graph is plotted it will have two peaks. The two peaks of the graph will show the local maximas, and they are the points from where the functions becomes decreasing from increasing. If a graph has two local maxima, it is known as a bimodal distribution of data.

Sometimes, two unimodal distributions are combined together to make a bimodal distribution:
Binomial Distribution

As we can see from this graph, it has got two points of maxima, that is, there are two points from where the graph will stop decreasing and start increasing.

Analysis

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Suppose we have a data set 5, 3, 1, 5, 2, 7, 5. Here, clearly 5 is repeated maximum number of times which makes us believe that 5 is the mode.
Again we take the data 2, 3, 5, 3, 2, 6, 2, 4, 3. Here both 3 and 2 are repeated three times in the data set. Hence, this data set has got two modes.
Two modes of the bimodal distribution  shows that the output from two streams are being mixed where both streams have different mean and standard deviation.

Bimodal distribution is a continuous distribution where two peaks are coming from a normal distribution. A continuous distribution can be done on a variable that is continuous which implies that the data can be measured on a measurement scale. For example length of certain entity is a continuous variable.

Histogram

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Histogram is a way to represent a data set graphically. It is a pictorial representation of the frequency of each number in the data set. It is easy to recognize if a histogram is bimodal or not, as a histogram having two peaks is bimodal.

It shows the formation of two groups in a given data set:

Binomial Distribution Bar Graph

This is a histogram image. In this image we can easily find out that there is only one maximum point, and hence this is a histogram for a unimodal distribution.
Binomial Distribution Histogram
In the above figure, we can easily find out that there are two maximas, that is, there are two peaks. Hence, this distribution is a bimodal distribution.


Six-Sigma

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Continuous distribution plays an important role in six sigma. Six sigma is a set of techniques and tools used by various organizations to detect and eliminate defects in any process, and improve process management. There are in total nine types of continuous distribution used in the six sigma, bimodal being one of them.

Fitting a  bimodal distribution

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To fit a bimodal distribution into a graph or histogram we can use various software tools available, R tool being one of them. There are several in-built commands in these tools to get the data set plotted as a graph or histogram. Openstat and Sage are some other such tools.

Example

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Suppose a site is being developed. There are two times the traffic will be high on this site, at 5 PM in evening and 3 AM in night. So there are two points of maxima which will make the distribution graph as bimodal.

Binomial Distribution Histogram Examples