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# The Simple Math Behind Crunching the Sizes of Crowds

How large was the crowd at the recent U.S. presidential inauguration? Or the inauguration 8 years ago? Or at last Saturday’s Women’s March in Washington D.C.? Keep on reading to find out how crowd sizes are estimated.

By
Jason Marshall, PhD
Episode #298

## Modern High-Tech Crowd Size Estimates

With really big events such as presidential inaugurations or political marches, modern technology offers some assistance to the crowd estimating experts of the world. Today you can launch a balloon or drone-borne camera system to hover over an event and take high resolution images of the crowd. But even with these technological advances, the best crowd estimates still ultimately come down to measuring the average density of people in a representative region of the crowd and then multiplying this value by the total area over which those people are spread out.

Modern technology offers some assistance to the crowd estimating experts of the world.

There are a few additional modern twists on the simple grid pattern technique in use today. For example, computers (and the humans that write the software they are running) are pretty good at looking at images and classifying different regions of those images based upon their densities. So instead of breaking up an image into a regular grid pattern, a computer can figure out the different amoeba-shaped regions in an image that share similar densities. Once you have such a map of the different regions, you can turn it into a more precise crowd count by calculating the actual density of humans in each region and performing the arithmetic problem just as before. The idea is the same, but the technique does provide more precise results.

## The Certainty and Uncertainty of Crowd Sizes

Even though we have the mathematical know-how to reliably estimate crowd sizes, you’ll still find that different groups can come up with very different estimates. Most of the time these differences don’t point to a problem with the math but are instead traceable to the biases of the person (or people) performing the estimate. For example, police, media, and event organizers often report different numbers. Why? Well, it’s fairly obvious that different groups might benefit by having larger or smaller numbers reported. Event organizers typically want to bolster their message, so they might be inclined to be “generous” with the assumptions they make in calculating their values.

While it’s good to keep all of this in mind, the real takeaway message here is that calculating crowd sizes isn’t all that complicated. The bottom line is that pictures don’t lie … and with the help of a bit of simple math, they provide all the information needed to accurately estimate crowd sizes.

## Wrap Up

Okay, that’s all the math we have time for today.

For more fun with math, please check out my book,The Math Dude’s Quick and Dirty Guide to Algebra. Also, remember to become a fan of The Math Dude on Facebook and to follow me on Twitter.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Crowd image from Shutterstock.