The idea, step by step
Plan before collecting
Specify the group, variable, units and period. Decide how units are selected, how observations are measured and how missing or unclear answers are handled. A journey-time question should define one-way or return travel, minutes and the relevant day. Use neutral wording and collect only information needed for the purpose.
Analyse the whole story
Check data, choose a suitable display and compare centre, spread and unusual values. Answer the original question in context, then state limitations of frame, size, timing or response. Suggest an improved next collection. Another person should be able to understand and repeat the rules; drawing a graph alone does not complete an investigation.
| Code | Minutes |
|---|---|
| A | 5 |
| B | 10 |
| C | 10 |
| D | 15 |
| E | 15 |
| F | 15 |
| G | 20 |
| H | 30 |
A common trap
The investigation ends when a graph is drawn.
Instead: A justified question, plan, interpretation and limitations are also needed.
See the thinking
Worked example 1
Summarise the supplied journey times.
| Code | Minutes |
|---|---|
| A | 5 |
| B | 10 |
| C | 10 |
| D | 15 |
| E | 15 |
| F | 15 |
| G | 20 |
| H | 30 |
- Ordered data: 5,10,10,15,15,15,20,30.
- Total 120; mean=120÷8=15.
- Middle values 15 and 15; mode 15; range=30−5=25.
Worked example 2
A study of all Year 8 travel times asks only students at a bus stop. Improve the plan.
- The bus-stop frame favours bus users.
- Select fairly from a complete Year 8 roll.
- Use the same one-way-time definition for everyone.
Check your understanding
Why is “everyone takes 15 minutes” not justified by the supplied data?
Show answer
Times vary from 5 to 30 minutes and only eight students were sampled.
A mean is a centre, not every observation or the whole population.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Write a precise question about Year 8 journeys to school.2 marks
- Choose a better frame: a complete Year 8 roll or a list from one bus stop. Explain.2 marks
- Find mean and range for the supplied journey data.3 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30 - Compare the mean and median in the supplied data.2 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30 - Suggest a display for the eight times and explain.2 marks
- Write a cautious conclusion and one improvement.3 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write a precise question about Year 8 journeys to school.2 marks
Define the variable, unit and target group.
For example: “How long in minutes is the usual one-way journey for Year 8 students enrolled here this term?” - Choose a better frame: a complete Year 8 roll or a list from one bus stop. Explain.2 marks
It can include walkers, cyclists, car passengers and bus users.
The complete Year 8 roll. - Find mean and range for the supplied journey data.3 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30 120÷8=15.
30−5=25.
Mean 15 minutes; range 25 minutes. - Compare the mean and median in the supplied data.2 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30 The fourth and fifth values are 15; the mean is 120÷8.
Both are 15 minutes. - Suggest a display for the eight times and explain.2 marks
Use a numerical display that retains variation.
A dot plot shows individual times, repeated values and spread. - Write a cautious conclusion and one improvement.3 marks
Original practice data: one-way journey times for eight sampled students Code Minutes A 5 B 10 C 10 D 15 E 15 F 15 G 20 H 30 Separate the sample result from the whole group and address small size.
These sampled times centre near 15 minutes but vary; a larger random sample across the year group would strengthen a population estimate.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.
Official curriculum source ↗