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Author: Jonathan Osters

This lesson will explain finding the mode of a data set.

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Source: Bimodal Distribution Graph, Creative Commons: Other charts and graphs created by the author

Video Transcription

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In this tutorial, you're going to learn how to interpret and calculate the mode of a dataset. So suppose that we have the heights of the Chicago Bulls basketball team listed in this list right here. I want to know what height would be considered typical for this team.

There's a couple of different ways we can go about it. We could find the mean, which would be add all these numbers up and divide by 15. Or, we could order them least to greatest and find the number that's in the middle. That would be the median.

Another way to do it would be to look at the values that appear most frequently. The mode is the most frequently occurring value in a dataset. In a quantitative data set like we have here, it's the most frequently occurring number or numbers, assuming that they do in fact occur more than once.

So 81 occurs here, here, here, and also here. But that's not the only number that occurs four times. In closer examination, we can see that 81 occurs four times, and 79 occurs four times. Unlike with means and medians, a distribution can have more than one mode. In this case, 79 and 81 are both modes.

Let's do a practice problem. A class has 12 students. And the grades from a 10-point quiz are listed here. Determine the mode. It shouldn't take you long to realize that the mode is nine. It appears four times, and nothing else appears more than three times. Seven appears three times. But that's not any more than nine.

We can also have the mode of a qualitative dataset. In a qualitative dataset, the mode is the most frequently occurring category or the largest category. It looks like in this example that there are several large categories here and here. But the largest category is biology. So biology would be the mode of this dataset.

And finally, one last thing to remember is that in a distribution, when you have it actually graphed out, you might have something that's multi-peaked. So there is a gap in between here. Not a full-on gap, but it does decrease very precipitously after this and rises again over here.

In a distribution, we would call both of these areas modes. This value over here, five, and again over here near eight, would be considered modes because they are the different peaks in the distribution. It might still be called bimodal, although in reality there is only the one mode here at eight. There is only one highest bar. Although we might still call this distribution bimodal.

So to recap, the mode is the most common value in a dataset. And by value, we might mean category if it's qualitative, or number if it's quantitative. There can be no mode if nothing appears more than one time, exactly one mode like we have in the quiz's example, or many modes like on the Chicago Bulls basketball team.

If no value appears more than once, again, there is no mode. And if several values appear an equal amount of plural times that are tied for the most, then they all are considered modes. So you can have more than one.

And modes may also refer to the peak or peaks of the distribution, even if they're not the tallest point in the distribution. If a distribution has many peaks, we might call them bimodal or multimodal. Good luck. And we'll see you next time.

Terms to Know

The most frequently appearing number in a set of quantitative data or most frequently occurring category in a set of qualitative data.