Keeping every value
A stem-and-leaf plot organizes numbers while keeping every data value visible. Each number is split into:
- a stem: the leading digit(s)
- a leaf: the last digit
Making one
Data: test scores 62, 67, 71, 74, 74, 78, 81, 83, 85, 85, 89, 90, 94
| Stem | Leaves |
|---|---|
| 6 | 2 7 |
| 7 | 1 4 4 8 |
| 8 | 1 3 5 5 9 |
| 9 | 0 4 |
Key: 7 | 4 means 74
Steps:
- Choose stems (here, the tens digits).
- Write each leaf next to its stem.
- Put leaves in order from smallest to largest.
- Add a key.
Reading the plot
- Minimum: 62; maximum: 94; range: 32
- Mode: 74 and 85 (both appear twice)
- Median: 13 values → 7th value = 81
- Shape: most scores are in the 70s and 80s.
Advantages
- Shows the distribution like a sideways histogram.
- Keeps the original values, so you can calculate the mean, median and mode exactly.
- Quick to make by hand for small data sets.
Decimals and larger numbers
Use the key to show place value.
- Heights in metres: 1 | 6 means 1.6 m
- Times: 12 | 3 means 12.3 s
- Large numbers: 24 | 5 means 245
Split stems
When leaves crowd onto a few stems, split each stem in two: one for leaves 0–4 and one for 5–9.
| Stem | Leaves |
|---|---|
| 7 | 1 4 4 |
| 7 | 8 |
| 8 | 1 3 |
| 8 | 5 5 9 |
Back-to-back plots
A back-to-back stem-and-leaf plot compares two groups. Leaves for one group go left (read right to left), the other right.
| Class A leaves | Stem | Class B leaves |
|---|---|---|
| 8 5 | 6 | 2 |
| 9 4 1 | 7 | 3 5 |
| 6 2 | 8 | 0 4 7 8 |
| 9 | 1 5 |
Key: 5 | 6 | 2 means 65 for Class A and 62 for Class B.
Class B’s scores are higher overall.
Worked examples
Example 1: What value is 5 | 8 if the key says 5 | 8 = 58? 58.
Example 2: Data: 23, 31, 35, 38, 42. Make the stems. 2, 3, 4.
Example 3: Median of leaves 3 | 1 4 6 and 4 | 0 2 (values 31, 34, 36, 40, 42)? 36.
Common mistakes
- Leaves not in order.
- Forgetting the key.
- Skipping a stem with no leaves: include it, so gaps in the data show.
Try it yourself
Data: 15, 22, 28, 31, 33, 33, 37, 40, 46
- Make a stem-and-leaf plot.
- Find the median.
- Find the mode.
- Find the range.
Answers: 1) 1 | 5; 2 | 2 8; 3 | 1 3 3 7; 4 | 0 6 2) 33 3) 33 4) 31
Quick recap
- A stem-and-leaf plot splits values into stems and leaves.
- Order the leaves and include a key.
- Use back-to-back plots to compare two groups.