The idea, step by step
Match the display to the question
A frequency table gives exact counts compactly. A column graph makes category sizes easy to compare. A pictograph can show a small count clearly when its key is simple. Choose a display that helps a reader answer your question, not just one that looks colourful.
| Fruit | Votes |
|---|---|
| Apple | 8 |
| Banana | 6 |
| Pear | 4 |
Make it readable and fair
A graph needs an informative title, category labels and an even scale. Start a simple count graph at zero. Make columns equally wide and leave equal gaps. If a pictograph key would need many awkward symbol parts, a column graph may be clearer.
A common trap
Using an uneven scale to fit a graph into a space.
Instead: Equal spaces must represent equal increases. Choose a suitable regular scale and label it.
See the thinking
An exact value
A teacher needs the exact number choosing each lunch option. What simple display is useful?
- Exact values should be easy to read.
- A frequency table lists each option beside its count.
A suitable key
A survey has category counts 4, 8 and 12. Choose a pictograph key that uses only whole symbols.
- Look for an equal group that divides all three counts.
- A key of 4 gives 1, 2 and 3 symbols.
Check your understanding
What three labels should a column graph include?
Show answer
A title, category labels and a labelled numbered scale.
They explain what the counts represent and how to read them.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Which display is usually clearer for comparing category counts at a glance: a long unsorted response list or a column graph?1 mark
- Choose a whole-symbol key for counts 6, 9 and 12.1 mark
- A vertical axis has equally spaced labels 0, 2, 5, 8. Explain the problem.2 marks
- Draw a column graph for the supplied fruit table. Include a title, categories and a scale.3 marks
Practice survey: favourite fruit Fruit Votes Apple 8 Banana 6 Pear 4 - A pictograph uses a key of 5 for counts 2, 3 and 4. Suggest a clearer choice.2 marks
- Why should all columns in a simple column graph have equal width?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Which display is usually clearer for comparing category counts at a glance: a long unsorted response list or a column graph?1 mark
Column heights make category sizes easier to compare.
A column graph. - Choose a whole-symbol key for counts 6, 9 and 12.1 mark
This needs 2, 3 and 4 symbols. A key of 1 also works.
One symbol represents 3 responses. - A vertical axis has equally spaced labels 0, 2, 5, 8. Explain the problem.2 marks
Use a constant step, such as 0, 2, 4, 6, 8.
The numerical increases are not equal even though the spaces are equal. - Draw a column graph for the supplied fruit table. Include a title, categories and a scale.3 marks
Practice survey: favourite fruit Fruit Votes Apple 8 Banana 6 Pear 4 A scale of 2 is convenient; other accurate regular scales are valid.
Columns should show Apple 8, Banana 6 and Pear 4, starting from zero with an even scale. - A pictograph uses a key of 5 for counts 2, 3 and 4. Suggest a clearer choice.2 marks
The key of 5 needs awkward fractions of symbols.
Use a key of 1 or a column graph. - Why should all columns in a simple column graph have equal width?2 marks
Unequal widths can make categories appear more or less important.
So their heights, rather than different widths, communicate the counts fairly.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Scaled pictographs/column graphs; data collection; suitable displays; distributions; survey investigations.
Official curriculum source ↗