The idea, step by step
Keep every observation
A stem-and-leaf plot splits each value into a stem and a leaf. Sort leaves in each row and include repeats: two leaves of 4 in the first row below mean two separate observations of 14 cm. Always state a key and units.
Dot plots also keep frequencies visible: each dot represents one observation. Stack repeated values vertically and space numerical positions evenly. Frequency tables are convenient when repeated dots would become crowded.
| Stem | Leaves |
|---|---|
| 1 | 2 4 4 7 |
| 2 | 0 1 4 4 |
Make comparisons fair
Use shared stems in a back-to-back stem plot, or a common horizontal scale for two dot plots. Label the groups. Otherwise a stretched axis can make one sample appear more variable just because of its display.
If sample sizes differ, raw frequency heights are not the same as proportions. Describe clusters, gaps, typical values and spread. Do not connect unordered observations as though they are a time series.
A common trap
Remove repeated leaves because the value is already shown.
Instead: Each repeat represents a separate observation; removing it changes the distribution.
See the thinking
Read the stem-and-leaf plot
Find the sample size, median and range.
| Stem | Leaves |
|---|---|
| 1 | 2 4 4 7 |
| 2 | 0 1 4 4 |
- There are eight leaves: 12, 14, 14, 17, 20, 21, 24, 24.
- Median cm.
- Range cm.
Two modes
For the plotted books-read data, find median and modes.
- There are seven observations, so the median is the fourth value, 4.
- The values 3 and 5 each occur twice, more often than the others.
- Both are modes; the largest repeated value is not the only mode.
Check your understanding
Stem 3 has leaves 1, 1, 5 and key 3 | 1 = 31. How many values?
Show answer
Three: 31, 31 and 35.
Both leaves of 1 count.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Construct an ordered stem-and-leaf plot for 21, 15, 19, 12, 21, 25. Include a key.3 marks
- Use the supplied plot. How many values equal 24, and how many values are there altogether?2 marks
Key: 1 | 4 means 14 cm. Each leaf is one measurement. Stem Leaves 1 2 4 4 7 2 0 1 4 4 - Draw a dot plot for 0, 1, 1, 2, 2, 2, 4 and state the mode.3 marks
- Values 1, 2, 3 have frequencies 4, 2, 3. Find the sample size.2 marks
- Why should two dot plots being compared use the same number scale?2 marks
- Samples have 10 and 30 observations. Does the taller frequency bar necessarily mean a larger proportion?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Construct an ordered stem-and-leaf plot for 21, 15, 19, 12, 21, 25. Include a key.3 marks
Order: 12, 15, 19, 21, 21, 25.
Use tens as stems and retain both 21 s.
Stem 1: 2 5 9. Stem 2: 1 1 5. Key 1 | 2 = 12. - Use the supplied plot. How many values equal 24, and how many values are there altogether?2 marks
Key: 1 | 4 means 14 cm. Each leaf is one measurement. Stem Leaves 1 2 4 4 7 2 0 1 4 4 Stem 2 contains two leaves of 4.
Count all eight leaves.
Two equal 24; eight altogether. - Draw a dot plot for 0, 1, 1, 2, 2, 2, 4 and state the mode.3 marks
Use equal numerical intervals.
Place one dot per observation; the tallest stack is at 2.
Stack counts are 1, 2, 3, 0, 1 at 0–4. Mode 2. - Values 1, 2, 3 have frequencies 4, 2, 3. Find the sample size.2 marks
Add frequencies, not the values.
.
9. - Why should two dot plots being compared use the same number scale?2 marks
A stretched axis changes the apparent spread.
A common scale makes comparison meaningful.
Equal distances should represent equal numerical differences. - Samples have 10 and 30 observations. Does the taller frequency bar necessarily mean a larger proportion?2 marks
4 out of 10 is 40%, but 9 out of 30 is 30%.
Compare relative frequencies when sizes differ.
No.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 9 sampling, comparative distributions, centre/spread/outliers, displays, critique and statistical investigations.
Official curriculum source ↗