Statistics How To

Bimodal Distribution: What is it?

Probability and Statistics >Basic Graphs and Charts

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Bimodal Distribution: Two Peaks.

Data distributions in statistics can have one peak, or they can have several peaks. The type of distribution you might be familiar with seeing is the normal distribution, or bell curve, which has one peak. The bimodal distribution has two peaks.

bimodal distribution

Bimodal distribution showing two normal distribution curves combined, to show peaks. Image credit: Maksim|Wikimedia Commons

The “bi” in bimodal distribution refers to “two” and modal refers to the peaks. It can seem a little confusing because in statistics, the term “mode” refers to the most common number. However, if you think about it, the peaks in any distribution are the most common number(s). The two peaks in a bimodal distribution also represent two local maximums; these are points where the data points stop increasing and start decreasing.

Q. What does a Bimodal Distribution tell you?

You’ve got two peaks of data, which usually indicates you’ve got two different groups. For example, exam scores tend to be normally distributed with a single peak. However, grades sometimes fall into a bimodal distribution with a lot of students getting A grades and a lot getting F grades. This can tell you that you are looking at two different groups of students. It could be that one group is underprepared for the class (perhaps because of a lack of previous classes). The other group may have overprepared.

Two peaks could also indicate your data is sinusoidal. If you suspect your data might be following a wave-like pattern, create a scatter plot or a run sequence plot to double-check for sinusoidal patterns. You could also make a lag plot; an elliptical pattern would confirm that the data is sinusoidal.

Sometimes, what appears to be a bimodal distribution is actually two unimodal (one-peaked) distributions graphed on the same axis. For example, this image shows a bimodal distribution for a group of students who did not study (the left peak) and a group of students who did study (on the right).
bimodal distribution 2

Unimodal Distributions.

Unimodal distributions have a single peak, or mode.

normal distribution with z-values on opposite sides of mean

Normal distribution (Bell curve) is unimodal.

 

bimodal distribution

Several unimodal distributions shown on the same graph. Image credit: Grendelkhan|Wikimedia commons.



Multimodal Distributions

Multimidal distributions have more than two peaks. If you can’t clearly find one peak or two peaks in a graph, the likelihood is that you either have a uniform distribution (where all the peaks are the same height) or a multimodal distribution, where there are several peaks of the same height.
multimodal2007


Tip: Although you might commonly associate “mode” with being the most frequently occurring number in a data set, the term mode actually has two meanings in statistics, which can be confusing: it can either be a local maximum in a chart, or it can be the most frequently occurring score in a chart. The “mode” in bimodal distribution means a local maximum in a chart (i.e. a local mode). The two terms actually mean the same thing, as the most commonly found item in a data set will have a peak. But when you’re trying to categorize graphs, it’s easier to think of the mode as a “peak” rather than a common number. This helps especially if the axes are not labeled.

Fun fact: While the bell curve is normally associated with grades (i.e. 5% of the class will get an A and 10% of the class will get a B), it’s also quite normal to have a bimodal distribution where roughly half of a class will do very well (getting As and Bs) and the other half of the class will receive poor grades (Ds and Fs). Bimodal distributions are very common in college freshman mathematics classes!

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Bimodal Distribution: What is it? was last modified: October 15th, 2017 by Andale

8 thoughts on “Bimodal Distribution: What is it?

  1. McKnight

    Sir,
    I have a question that says: find the Mode of the data below:
    2,3,3,4,2,6,3,3,4,4,4.
    Options
    A) 1.5
    B) 2.5
    C) 3.5
    D) 4.5.

    I am confused of this question and I have series of it in my test.
    Thanks.

  2. Andale Post author

    Hi, Karen,
    What was the information you were looking for? If we need to add something, let me know!
    Regards,
    Stephanie

  3. Lino Ater

    I have this question to find mode but I was absolutely confused in my last semester.

    Mark. No of student s
    0-10. 3
    10-20. 5
    20-30. 7
    30-40. 10
    40-50. 12
    50-60. 15
    60-70. 12
    70-80. 6
    80-90. 2
    90-100. 8

  4. Andale Post author

    The mode is just the most common number. As 15 students scored between 40-50, that’s the most common.

  5. Carol

    I have a question that has
    marks of students
    0-10 8
    10-20 7
    20-30 15
    30-40 5
    40-50 15
    How do i find the mode?