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What Are Stem-and-Leaf Plots?

How do you make stem-and-leaf plots? Why might you want to? How are they related to the stems and leaves that fall from trees?

By
Jason Marshall, PhD
5-minute read
Episode #264

Fall leavesFall has finally arrived in Los Angeles, which really just means that daytime highs have “plummeted” from the 80s down into the 60s. Brrr! (Or not.) Anyway, with the change in season comes the annual falling of the leaves from the fruit trees in my backyard. Although the cherries and apricots seem to be holding out for even colder weather before slipping into their seasonal slumber, this week the persimmon and plum trees gave up and shed their summertime duds for a sparser look.

Earlier in the week, in the midst of an action-packed game of bounce-the-ball-off-daddy’s-head, my daughter stopped to pick up one of these leaves. She then picked up another, and another, and another, and … well, you get the picture. A pile began to grow in our backyard … and then in the house. Throughout the week these piles grew, and they now include leaves not just from our backyard, but from the whole neighborhood, local parks, and pretty much anywhere else we've ventured.

Clearly she thinks that leaves are really cool, and I do too. (Don’t you?) Not only are they beautiful and fascinating little things (just ask any tree), there’s even a type of plot—called the stem-and-leaf plot—named after them! OK, that last thing probably isn’t the coolest thing about leaves, but I do think it’s pretty nifty.

With all of these leaves in my life right now, I can’t help but want to talk about them today—which is exactly what we’re going to do. And given that this is a show about math and data and all of the things that can be done with math to analyze data, over the next few weeks we’re going to talk about just what a stem-and-leaf plot is, what it can show you, and why it’s named after all of those beautiful leaves my daughter is collecting.

Why Is it Useful to Plot Data?

Before we start talking about the specifics of the stem-and-leaf plot and all that it can do to enhance your data-analyzing life, let’s take a minute to talk about plots in general. In particular, let’s talk about why making any kind of plot—and there are lots of different kinds that you can make—is a useful thing to do in the first place.

The reason is simple, and it’s best explained with an example. Let’s say I’m looking through my daughter’s piles of leaves and decide that I’d really like to measure the height and width of each leaf. Why would I want to do that? I have no idea … but stick with me. Imagine I grab a ruler and start measuring leaves one-by-one, writing the height and width in nice neat columns on a big sheet of paper.

After collecting 100 or so sets of measurements, I’d have 100 or so lines of data. And I might start to wonder: What’s the most common width? Or height? Are they clustered around some value or are they all spread out? Is there any relationship between the widths and heights of leaves?

A plot can make the answer immediately clear to see.

Looking at the sheet of paper full of numbers, it’s hard to quickly answer any of these questions. But if we make a plot of the width of leaves on the x-axis versus the height of leaves on the y-axis, we’ll immediately be able to visually see if there is a relationship between the width and height. If the points all fall along some sort of a line, then the answer is “Yes!” But if they’re instead scattered all over the place, the answer is “No.” Either way, a plot can make the answer immediately clear to see.

If we make a stem-and-leaf plot, we’ll quickly be able to answer the first few questions we asked: What's the most common leaf width? Or height? And are these values clustered around some number or are they spread out? Let’s make the plot and find out.

What Is a Stem-and-Leaf Plot?

Making a stem-and-leaf plot is really quite simple. In fact, it’s not even a plot per se—it’s more of a diagram or a table. But people call it a plot so we’ll do the same. All you do to make this plot is take your collection of data—let’s say it’s just the widths of those 100 leaves—and write them using a special two-column format.

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About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.