Creating Stem-and-Leaf Displays- Tutorial
What Is a Stem-and-Leaf Display?
A stem-and-leaf display (or stem-and-leaf plot) is a simple way to organize raw numbers so you can actually see the distribution of your data. It's not fancy. No software required. Just pen, paper, and basic math skills.
The "stem" is the leading digit(s), and the "leaf" is the trailing digit. That's it. Nothing complicated.
Why bother? Because looking at a list of 50 numbers tells you nothing. A stem-and-leaf plot shows you the shape of your data instantly. You can spot clusters, gaps, and outliers without doing any calculations.
How to Read a Stem-and-Leaf Plot
Before you create one, you need to know how to read one. Here's a quick example:
Test Scores (out of 100):
Stem | Leaves 5 | 5 7 9 6 | 2 4 4 8 7 | 1 3 5 5 6 8 8 | 0 2 4 6 9 9 | 1 3
The stem "7" with leaves "1 3 5 5 6 8" means six students scored in the 70s: 71, 73, 75, 75, 76, and 78.
Reading is straightforward once you get the hang of it. The stems are always listed in order from smallest to largest, and the leaves are sorted within each stem row.
How to Create a Stem-and-Leaf Display (Step by Step)
Let's walk through this with real data. Here's a dataset of 20 daily temperatures (in degrees Fahrenheit):
Data: 72, 68, 85, 91, 73, 79, 88, 94, 67, 82, 76, 89, 95, 71, 84, 77, 86, 92, 69, 80
Step 1: Find the Range
Smallest value: 67. Largest value: 95. Your stems will span from 6 to 9.
Step 2: Determine Your Stems
For two-digit numbers, the stem is the tens digit. So:
- 67 → stem 6, leaf 7
- 72 → stem 7, leaf 2
- 91 → stem 9, leaf 1
Step 3: List the Stems First
Write the stems in a vertical column, smallest to largest:
6 | 7 | 8 | 9 |
Step 4: Add the Leaves
Go through each number and write the ones digit next to its stem. Don't worry about order yet.
6 | 7 8 9 7 | 2 3 1 6 9 8 | 5 8 4 6 9 | 1 4 5 2
Step 5: Sort the Leaves
Now arrange each row's leaves in ascending order:
6 | 7 8 9 7 | 1 2 3 6 9 8 | 4 5 6 8 9 | 1 2 4 5
Done. That's your stem-and-leaf display.
Reading Your Plot
From the plot above, you can immediately see:
- The most common temperatures were in the 70s and 80s
- No temperatures in the 60s below 67
- The distribution is fairly even across the 70s, 80s, and 90s
You can also reconstruct the original data if needed. Just match each stem with its leaves.
Back-to-Back Stem-and-Leaf Plots
Want to compare two datasets? Use a back-to-back plot. The stems go in the middle, one set of leaves extends left, another extends right.
Week A | Stem | Week B
4 2 1 | 6 | 3 5
9 7 5 3 2 | 7 | 4 6 8
8 6 4 | 8 | 5 7 9
| 9 | 2
This makes it easy to compare two groups side by side. Useful for before/after scenarios, male/female comparisons, or any two distributions you want to contrast.
When to Use Stem-and-Leaf Plots
These work best when:
- You have less than 100 data points
- Your data is discrete and numerical
- You need to see the actual values, not just counts
- You want a quick visual of the distribution shape
They don't work well for categorical data, huge datasets, or when you need to present findings to non-technical audiences.
Stem-and-Leaf vs. Other Displays
Here's how stem-and-leaf plots compare to common alternatives:
| Feature | Stem-and-Leaf | Histogram | Box Plot |
|---|---|---|---|
| Shows exact values | ✅ Yes | ❌ No | ❌ No |
| Easy to construct by hand | ✅ Yes | ⚠️ Some math needed | ⚠️ Need to find quartiles |
| Good for small datasets | ✅ Yes | ⚠️ Can look sparse | ❌ Not ideal |
| Good for large datasets | ❌ Gets messy | ✅ Yes | ✅ Yes |
| Shows distribution shape | ✅ Yes | ✅ Yes | ⚠️ Limited |
| Good for presentations | ❌ Looks informal | ✅ Yes | ✅ Yes |
If you need to show your work to someone else, use a histogram or box plot. If you're exploring data for yourself, the stem-and-leaf is faster and more informative.
Common Mistakes to Avoid
1. Forgetting to sort leaves. Unsorted leaves make the plot hard to read. Always sort.
2. Using too many or too few stems. If every stem has one or two leaves, you have too many stems. If stems have 15+ leaves each, you need more detail.
3. Mixing up stem units. If your data ranges from 100-999, your stem might be the hundreds digit. Be consistent and label your plot clearly.
4. Skipping the key/legend. Always include "5 | 2 = 52" so readers know how to interpret the plot.
Quick Reference: Creating a Stem-and-Leaf Plot
- Organize your data from smallest to largest (mentally or on paper)
- Identify the stem (usually the leading digit(s))
- Draw a vertical line
- List all stems in order
- Plot each leaf next to its stem
- Sort leaves within each row
- Add a key explaining the stem and leaf units
Total time for a dataset of 20-30 numbers: about 2-3 minutes.
When Stem-and-Leaf Displays Fall Short
They're not magic. For datasets over 100 points, the plot becomes unreadable. For continuous data like heights measured to the nearest millimeter, you'll end up with one leaf per stem and gain nothing.
They're also not great for showing percentages, proportions, or comparing groups of wildly different sizes. If you need any of that, use a histogram or statistical software.
Bottom line: stem-and-leaf plots are a quick, dirty, effective tool for small-to-medium datasets when you want to see the actual numbers, not just the shape. They won't win any design awards, but they'll give you answers fast.