The idea, step by step
Keep the observations visible
In a dot plot, place one dot for each observation above its value. Repeated values stack vertically; do not spread them to nearby values. The horizontal axis gives the measured or counted value, while the number of stacked dots shows frequency.
A dot plot makes clusters, gaps and unusual values visible. Count all dots to check that the display includes the complete dataset.
Read the key before the leaves
A stem-and-leaf plot splits each observation into a stem and a leaf. With a leaf unit of 1 cm, 1 | 2 means 12 cm. Order the leaves within each row, keep repetitions and show units or a key.
The same symbols can mean something different with another key: 1 | 2 might mean 1.2 m. An empty stem can show a gap. The key is part of the graph, not decoration.
| Stem | Leaves |
|---|---|
| 1 | 1 2 2 3 5 8 |
| 2 | 0 1 1 4 |
A common trap
A repeated leaf should be written only once.
Instead: Every observation needs its own leaf. Repetitions carry frequency information.
See the thinking
Read repeated dots
How many students in the dot plot borrowed four books, and how many borrowed at least six?
- Three dots above 4 mean three students borrowed four books.
- At least six includes 6 and 7, each with one dot.
Construct an ordered stem plot
Show 24, 25, 29, 31, 31, 36 in a stem-and-leaf table with leaf unit 1.
| Stem | Leaves |
|---|---|
| 2 | 4 5 9 |
| 3 | 1 1 6 |
- Use tens as stems 2 and 3.
- Stem 2 has ordered leaves 4, 5, 9.
- Keep both observations of 31: stem 3 has leaves 1, 1, 6.
Check your understanding
A plot has key 3 | 7 = 3.7 kg. What does 4 | 2 mean?
Show answer
4.2 kg.
The stem gives whole kilograms and the leaf tenths of a kilogram.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- List all values shown by the stem plot.2 marks
Leaf unit = 1 cm; key 1 | 2 means 12 cm Stem Leaves 1 1 2 2 3 5 8 2 0 1 1 4 - How many observations are in the stem plot?2 marks
Leaf unit = 1 cm; key 1 | 2 means 12 cm Stem Leaves 1 1 2 2 3 5 8 2 0 1 1 4 - Construct an ordered stem plot for 14, 18, 18, 21, 23, 25. Include a key.2 marks
- State the most frequent value in the dot plot.2 marks
- How many students in the dot plot borrowed fewer than four books?2 marks
- A stem plot shows 5 | 3 but gives no key or units. Explain why it is incomplete.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- List all values shown by the stem plot.2 marks
Leaf unit = 1 cm; key 1 | 2 means 12 cm Stem Leaves 1 1 2 2 3 5 8 2 0 1 1 4 Read every leaf, including repeated 2s and 1s.
11, 12, 12, 13, 15, 18, 20, 21, 21, 24 cm. - How many observations are in the stem plot?2 marks
Leaf unit = 1 cm; key 1 | 2 means 12 cm Stem Leaves 1 1 2 2 3 5 8 2 0 1 1 4 There are 6 leaves in the first row and 4 in the second: 6+4=10.
10. - Construct an ordered stem plot for 14, 18, 18, 21, 23, 25. Include a key.2 marks
Separate tens and ones.
Order the leaves and retain both 18s.
1 | 4 8 8; 2 | 1 3 5; key 1 | 4 = 14. - State the most frequent value in the dot plot.2 marks
Three dots stack above 4, more than above any other value.
4 books. - How many students in the dot plot borrowed fewer than four books?2 marks
The values below 4 are 2, 2 and 3.
3 students. - A stem plot shows 5 | 3 but gives no key or units. Explain why it is incomplete.2 marks
A key and units define the value represented by each stem–leaf combination.
The reader cannot know whether it means 53, 5.3 or another scale, or what is measured.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Mathematics Curriculum
Year 7 statistical variables, representations, summary statistics, outliers and an original small investigation; deeper sampling methods develop in Year 8.
Official curriculum source ↗