The idea, step by step
Start with the question
A bar chart compares frequencies for categories such as travel method. Separate bars show distinct groups. A dot plot or stem-and-leaf display is useful for a small numerical sample because it keeps individual values and repeats. Grouping larger numerical sets can reveal shape, but loses detail inside each interval.
For change through time, place time on the horizontal axis in chronological order, with proportional spacing. A line can reveal a trend but does not prove exactly what happened between observation times.
Design for comparison
Compare numerical groups on the same horizontal scale. When sample sizes differ, consider relative frequencies instead of raw counts. Always provide labels, units, keys and sensible intervals so that a reader can recover the intended meaning.
There may be more than one suitable display. Explain your choice in terms of the question. Tables are often best for looking up exact figures, while graphs help reveal patterns. Avoid adding decoration that makes data harder to read.
A common trap
All displays communicate the same information equally well.
Instead: A display may hide exact values, timing or sample-size differences; choose it for the purpose.
See the thinking
Category data
Twenty students choose their favourite fruit. Which display suits the responses?
- Favourite fruit is categorical.
- Count each choice in a frequency table.
- Use a labelled bar chart with separate equal-width bars and a count axis starting at zero.
Two small numerical samples
You have jump distances for 12 students in each of two classes. You want to compare distributions.
- Jump distance is numerical; both samples are small.
- Use two dot plots on one distance scale, or a back-to-back stem-and-leaf display.
- Compare centre, spread and overlap, not just the best jump.
Check your understanding
What belongs on the horizontal axis for daily rainfall across a month?
Show answer
Date or day in order, with equal spacing for equal times.
The display is intended to show change through time.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Choose a display for numbers of students travelling by bus, car, bicycle or walking. Explain.2 marks
- Choose a display for 14 hand-span measurements while retaining exact individual values.2 marks
- Why might relative-frequency bars help compare samples of 20 and 100?2 marks
- Use the graph. Which day has the most visits, and how much do visits fall the next day?2 marks
- A display groups ages into ten-year intervals. What detail is lost?2 marks
- A report needs exact enrolment counts. Should it provide only a graph? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Choose a display for numbers of students travelling by bus, car, bicycle or walking. Explain.2 marks
Travel methods are categories.
Count responses and use separate bars with a labelled frequency axis.
A bar chart. - Choose a display for 14 hand-span measurements while retaining exact individual values.2 marks
The sample is small and numerical.
These displays retain repeated values and individual observations.
A dot plot or stem-and-leaf plot. - Why might relative-frequency bars help compare samples of 20 and 100?2 marks
Divide counts by the sample total.
Raw counts may mainly show the sample-size difference.
They compare proportions on a common basis. - Use the graph. Which day has the most visits, and how much do visits fall the next day?2 marks
Thursday has 24 visits; Friday has 21.
.
Thursday; a fall of 3 visits. - A display groups ages into ten-year intervals. What detail is lost?2 marks
Different ages share the same group.
Grouping reveals broad shape but hides fine detail.
Exact ages and variation within each interval. - A report needs exact enrolment counts. Should it provide only a graph? Explain.2 marks
A table allows direct lookup.
A graph alone may require estimating from a scale.
Include a table of exact counts, possibly alongside a graph.
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 ↗