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# How to Use Stem-and-Leaf Plots

Why are stem-and-leaf plots useful? How are they related to the kind of stems and leaves that fall from trees this time of year?

By
Jason Marshall, PhD
Episode #265

## How to Use Stem-and-Leaf Plots

If you instead start by creating a stem-and-leaf plot, you’ll be able to find the median and especially the mode a lot more easily. The organization provided by the two columns of the stem-and-leaf plot makes it a little bit easier to figure out which number is in the middle of the data set (that’s the median), and a whole lot easier to find the mode.

Why the big improvement in finding the mode? If you think about it, you’ll see that the organization provided by the plot makes it easy to see which “leaf” occurs most frequently. And that most frequently occurring "leaf" (for a given "stem") must be the mode of the data set. So stem-and-leaf plots are great for investigating the frequency with which different values occur.

Stem-and-leaf plots are great for investigating the frequency with which different values occur.

What if you were even more curious about leaf widths and wanted to know if most of the widths are clustered around the most common value? Or if they're spread out over a broad range of values? In other words, what if you also wanted to know about the shape of the distribution of leaf widths? A stem-and-leaf plot can help here too since it will immediately show you if most of the values are clustered together, or if they’re evenly spread out over the different “stems,” or anything else. So stem-and-leaf plots are also great for investigating the “shape" of your data set.

## Alternatives to the Stem-and-Leaf Plot

While stem-and-leaf plots are a useful tool, they’re not the only way you can investigate these types of questions about a set of data. The other big technique for studying this type of data—in particular for studying the distribution or shape of a data set—is to use something called a histogram.

What’s that? Well, unfortunately—as so often happens—we’re all out of time for today. So the answer to that question will have to wait until next time.

## Wrap Up

In the meantime, for more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

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!

Leaf image from Shutterstock.