What is the difference between unimodal and bimodal distribution

Every day we encounter random variables in every aspect of our lives. These random variables play a vital role in most fields of research including chemistry, engineering, and physics, and most importantly in management and social sciences. 

These are analyzed and measured according to their probabilistic and statistical properties, the basic characteristic of which is the distribution function. 

In statistics, when we use the term distribution, we usually mean probability distribution. The assignments show the possible value variables and how often they occur. 

The first characteristic of a variable's data distribution is its mode, which refers to the value of the variable that occurs most frequently in a set of data. 

Simply put, the mode is determined by the number of peaks the distribution contains. The mode of the distribution can be unimodal or bimodal, depending on the frequency of occurrence of values. 

Let us briefly understand unimodal and bimodal distributions and try to understand the main differences between the two.

What is a unimodal distribution?

As the name suggests, a unimodal distribution is a unimodal distribution, which means that one value occurs more often than others. The shape of the distribution usually has a clear peak. 

A unimodal distribution is one that has a single clearly visible peak or single most frequent value. This means that the shape of the distribution has only one major high. 

After the value increases to that point, the value starts to decrease. The most common example of a unimodal distribution is the normal distribution. Sometimes the high is in the center, sometimes it peaks on the right or left. 

Mode refers to the most frequently observed value in the data. Unimodal distributions are not necessarily symmetric; they are likely to be asymmetric or skewed. 

A left-skewed distribution is when the mean is skewed to the left, while a right-skewed distribution is when the mean is skewed to the right.

What is a bimodal distribution?

If a distribution has two fairly equal highs, it is called a bimodal distribution. It is the distribution with the most frequent occurrences of the two values. The figure resembles the two humps on a camel's back. 

Bi means two, so doublet means two modes. A bimodal distribution is a distribution with two visible peaks or two frequent values with a gap between them. 

Any bump in the data is a pattern, so the bimodal distribution has two distinct clear patterns. The mode refers to the most frequently repeated number, which is also the peak in the distribution. 

Therefore, a bimodal distribution has the two most frequently repeated values in the distribution. There is usually a large gap between the two modes, and the distribution contains more data than the other modes.

What is the difference between the unimodal and bimodal distribution

Definition

 – The mode of the distribution can be unimodal or bimodal, depending on the frequency of occurrence of values. Unimodal is a unimodal distribution in which one value occurs more frequently than the others. 

It is a distribution with a single clearly visible peak or single most frequent value. On the other hand, a bimodal distribution is a distribution where two values occur with the highest frequency, which means there is a gap between two frequent values.

Shape

– The distribution shape in a unimodal distribution has only one major high. Sometimes the high is in the center, sometimes it peaks on the right or left. The high point is the most frequently observed value in the data, called the mode. 

A bimodal distribution, on the other hand, is a distribution with two fairly equal highs (or patterns). There is usually a large gap between the two modes, and the distribution contains more data than the other modes.

Example

– One of the best examples of a unimodal distribution is the standard normal distribution, which has a mean of 0 and a standard deviation of 1. Other examples include chi-square, Cauchy, exponential, Student's t, etc. 

A real-world example of a bimodal distribution is the number of vehicles crossing London Bridge by the time of day. You can see peak times during peak hours (around 8 and 6) with less traffic in between. If you put the numbers on the graph, you'll notice multiple peaks.

Generalize

Simply put, a unimodal distribution is a distribution that has only one peak or one major high. It might be described as bell-shaped, as it is highest in the middle, and the shape of the bell slopes downward as it moves away from the top, like a bell. One of the best examples of a unimodal distribution is the standard normal distribution. 

On the other hand, bimodal means two modes, so a bimodal distribution is a distribution with two peaks or two major highs, each peak is called a local maximum and the valley between the two peaks is called a local minimum value.

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