How a stem-and-leaf plot works
A stem-and-leaf plot splits every number into a stem (the leading digits) and a leaf (the last digit). Stems are listed once, in order; leaves are written beside them. The result looks like a histogram turned on its side, but every original value can still be read from it.
Example
Scores: 52, 58, 61, 64, 64, 67, 69, 70, 71, 73, 75, 75, 76, 78, 80, 82.
| Stem | Leaves |
|---|---|
| 5 | 2 8 |
| 6 | 1 4 4 7 9 |
| 7 | 0 1 3 5 5 6 8 |
| 8 | 0 2 |
Key: 5 | 2 = 52. Reading it, most scores are in the 70s, the modes are 64 and 75 (each appears twice), and the median of these 16 values is the average of the 8th and 9th: (70 + 71) ÷ 2 = 70.5.
Tips for a good stem-and-leaf plot
- Always include a key, so readers know whether 4 | 7 means 47 or 4.7.
- Keep empty stems. If no values are in the 30s, keep the 3 stem with no leaves. Gaps are part of the shape.
- Order the leaves from smallest to largest, which makes the median and quartiles easy to count.
- Split stems when a few rows hold most of the leaves.
- Best for roughly 15–100 values. For more, a histogram is clearer.
Need the median and quartiles worked out? Use the five-number summary calculator.
Worked example: a back-to-back plot
Load “Back-to-back” above. Boys’ scores are on the left and girls’ on the right of one shared stem column. Reading across the 6 stem: the boys have 60, 62, 62, 65, 68 and the girls 61, 63, 64, 66, 69. Overall the girls’ leaves extend further down the plot (into the 70s and 80s), so their scores are higher on average, while both groups start in the 40s.
Common mistakes to avoid
- Leaving out the key. Without it, nobody knows whether 4 | 7 means 47, 4.7 or 470.
- Skipping empty stems. Keep stems with no leaves; the gaps are part of the shape.
- Unsorted leaves. Order the leaves so the median and quartiles can be counted directly.
- Leaves with two digits. Each leaf is a single digit. Round or change the leaf unit instead.
Do it in other software
| Software | How |
|---|---|
| R | stem(x) prints a stem-and-leaf plot in the console. |
| Minitab | Graph › Stem-and-Leaf. |
| Excel / Google Sheets | No built-in option. Use =INT(x/10) for stems and =MOD(x,10) for leaves, or use this tool. |
Related tools: Dot Plot Maker, Histogram Maker, Five-Number Summary Calculator, Mean, Median & Mode Calculator and Relative Frequency Histogram.