Source: Bimodal Height Distribution; Creative Commons: http://en.wikipedia.org/wiki/File:BimodalAnts.png Other graphs created by the author
In this tutorial, you're going to learn about unimodal distributions versus bimodal distributions. Uni means one. Bi means two. Modal means the number of modes each distribution has.
So oftentimes distributions will have a clear peak to their shape. And they won't peak anywhere but just one place on the distribution. So for instance, this distribution has a peak right here. This distribution peaks further to the right. And the next distribution peaks further to the left.
But they all have a clear peak. All of these are called a unimodal distributions. And the tallest bar is called the mode. So this is the mode here, this is the mode there, and this is the mode here.
You might, though, have a distribution that will have two distinct regions with lots of data points, and a gap in the middle. When this happens, the two peaks form on the distribution. And those are both called modes. So a distribution like this is called bimodal.
So there's a peak here and another peak over here. Now technically, there's only one bin here that's the mode. It's the tallest one. But these are very tall relative to the others around them.
So they're sort of local modes. And there are two of them. A peak, a gap, and a peak.
Now sometimes you have a distribution that appears bimodal-- one here, and then a gap, and then another one here. It appears to be bimodal, but upon further examination of heights, it's possible that you have to do different distributions that happened to be graphed on the same set of axes.
So there might be some hidden variable that causes the bimodality. And when viewed separately, you end up with two unimodal distributions. They just happened to be graphed on the same set of axes.
You might also encounter something like this, if there were something like test scores with students who didn't study versus students who did study. You might find that there are two, kind of, extremes for that distribution of test scores.
And any distribution with more than two peaks is called multimodal. This distribution, for instance, has four peaks. But you can have the same issues with these, as you did with the bimodal distribution, in that it may be multiple distributions graphed on the same set of axes.
And so to recap, some distributions are unimodal, that's single peaked distributions. And others are bimodal, that are clearly double peaked. And some, even, that are multimodal.
Now sometimes, a bimodal distribution is simply to unimodal distributions graphed together. And oftentimes, there's a reason for the bimodality.
So we talked about unimodal, single peaked, bimodal, little double peaked, and multimodal, multiple peaks. Good luck, and we'll see you next time.
A distribution where one value or bin contains more data than the other values or bins.
A distribution where there are two distinct values or bins that contain more data than the others, usually separated by a gap.
A distribution where there are many values or bins that contain more data than other nearby bins, usually separated by gaps.