Social scientists rely on the normal distribution all the time. This classic “bell curve” shape is so important because it fits all kinds of patterns in human behavior, from measures of public opinion to scores on standardized tests.

But it can be difficult to teach the normal distribution in social statistics, because at the core it is a theory about patterns we see in the data. If you’re interested in studying people in their social worlds, it can be more helpful to see how the bell curve emerges from real world examples.

One of the best ways to illustrate this is the “Galton Board,” a desk toy that lets you watch the normal distribution emerge from a random drop of ball-bearings. Check out the video below or a slow motion gif here.

The Galton Board is cool, but I’m also always on the lookout for normal distributions “in the wild.” There are places where you can see the distribution in real patterns of social behavior, rather than simulating them in a controlled environment. My absolute favorite example comes from Ed Burmila:

The wear patterns here show exactly what we would expect a normal distribution to tell us about weightlifting. More people use the machine at a middle weight setting for the average strength, and the extreme choices are less common. Not all social behavior follows this pattern, but when we find cases that do, our techniques to analyze that behavior are fairly simple.

Another cool example is grocery shelves. Because stores like to keep popular products together and right in front of your face (the maxim is “eye level is buy level“), they tend to stock in a normally-distributed pattern with popular stuff right in the middle. We don’t necessarily see this in action until there is a big sale or a rush in an emergency. When stores can’t restock in time, you can see a kind of bell curve emerge on the empty shelves. Products that are high up or off to the side are a little less likely to be picked over.

Paul Swansen, Flickr CC

Have you seen normal distributions out in the wild? Send them my way and I might feature them in a future post!

Evan Stewart is an assistant professor of sociology at University of Massachusetts Boston. You can follow his work at his website, or on BlueSky.