Split each value into a stem and a leaf
The value 23 has stem 2 and leaf 3. The value 31 has stem 3 and leaf 1.
The stem holds every digit except the last one, which becomes the leaf.
Year 7
Construct and interpret stem-and-leaf diagrams
Build a stem-and-leaf diagram from raw data, read values back off it correctly, and use it to find the mode, median and range.
Lesson overview
Statistics and data - stem-and-leaf diagrams
A stem-and-leaf diagram sorts data while keeping every original value visible. Each number is split into a 'stem' (all digits except the last) and a 'leaf' (the last digit). Leaves are always written in order along each stem row, and a key such as '2 | 3 means 23' shows how to read the diagram.
Build the diagram from raw data
12 pupils recorded these ages in months over their target: 19, 22, 23, 24, 25, 27, 28, 31, 31, 33, 34, 40.
| Stem | Leaves |
|---|---|
| 1 | 9 |
| 2 | 2 3 4 5 7 8 |
| 3 | 1 1 3 4 |
| 4 | 0 |
Key: 1 | 9 means 19
Leaves are written in order along each stem row, smallest to largest.
Use the diagram to find averages and range
From the diagram above, the smallest value is 19 and the largest is 40.
appears twice
average of the 6th and 7th values
With 12 values, the median is the average of the 6th and 7th values once the data is ordered.
Worked example
Find the median, mode and range of these 10 test scores: 12, 15, 18, 21, 23, 23, 27, 29, 32, 35.
| Stem | Leaves |
|---|---|
| 1 | 2 5 8 |
| 2 | 1 3 3 7 9 |
| 3 | 2 5 |
Key: 1 | 2 means 12 marks
- Split every score into a stem (tens) and a leaf (units), and order the leaves along each row.
- There are 10 scores, so the median is the average of the 5th and 6th values once ordered: 23 and 23.
- The mode is 23, since it is the only value that appears twice.
- The range is the largest value minus the smallest: 35 - 12 = 23.
Try it
Split each value into a stem and a leaf, keep the leaves in order, then read the diagram carefully for averages and range.
Question 1
The value 34 is split into a stem and a leaf. What is the leaf?
Question 2
A stem-and-leaf diagram has the key '2 | 3 means 23'. What value does '4 | 1' represent?
Question 3
This stem-and-leaf diagram shows 9 values: 11, 14, 14, 18, 22, 25, 29, 31, 36. What is the median?
| Stem | Leaves |
|---|---|
| 1 | 1 4 4 8 |
| 2 | 2 5 9 |
| 3 | 1 6 |
Key: 1 | 1 means 11
Question 4
For the data 8, 12, 12, 15, 19, what is the mode?
| Stem | Leaves |
|---|---|
| 0 | 8 |
| 1 | 2 2 5 9 |
Key: 0 | 8 means 8
Question 5
For the data 21, 24, 27, 30, 33, what is the range?
| Stem | Leaves |
|---|---|
| 2 | 1 4 7 |
| 3 | 0 3 |
Key: 2 | 1 means 21
Common mistakes
Watch for these when working through the lesson.
- Writing the leaves in the order they were collected instead of sorting them along each row.
- Forgetting to check the key, which shows how a stem and a leaf combine back into a value.
- Miscounting the middle position when finding the median from an even number of values.
Related topics
These ideas fit closely with this lesson.
- Calculate mode, median, mean and range from small data sets.
- Construct bar charts, pictograms and frequency tables.
- Plan, present and interpret a simple survey.