Understand the idea.
Plan before collecting
Begin with a precise investigation question naming the population, variable and groups. Decide how each measurement will be collected before seeing results, including units, the observation period and treatment of unusual events. Fair selection is needed within each comparison group.
Use the same wording and measurement conditions, record response rates and collect only information needed for the question. Anonymous codes are often sufficient. Obtain suitable permission for personal information and protect participants’ privacy when storing and reporting the data.
Analyse and review
Check units, impossible values, missing responses and possible recording mistakes before analysis. Investigate suspicious observations and document confirmed corrections. Choose a useful display, calculate centre and spread, then answer the original question with numerical evidence in context.
Report limits as well as results. Small or unrepresentative samples restrict generalisation, and unmatched groups may differ for other reasons. For journey times, distance may affect the comparison; comparing similar distances or collecting a larger fair sample can improve the evidence.
| Walk (min) | Bus (min) |
|---|---|
| 8 | 5 |
| 10 | 8 |
| 10 | 12 |
| 12 | 12 |
| 15 | 15 |
| 17 | 20 |
See the method in action.
Compare journey times
Use the supplied walking and bus times to compare the samples.
| Walk (min) | Bus (min) |
|---|---|
| 8 | 5 |
| 10 | 8 |
| 10 | 12 |
| 12 | 12 |
| 15 | 15 |
| 17 | 20 |
Worked solution
- 1
Calculate each sample mean.
Both samples total minutes and contain six observations.
- 2
Average each middle pair.
With six ordered observations, the median averages positions three and four.
- 3
Calculate the ranges.
Subtract each sample’s minimum from its maximum.
- 4
State a sample-based comparison.
The means are equal. Walking has a one-minute lower median and a smaller range in these samples, but the groups overlap and the rows are not matched students.
Both means 12; walking median 11/range 9; bus median 12/range 15.
Improve a conclusion
A report says: Bus travel is always slower because its sample median is 12 rather than 11. Improve it.
Worked solution
- 1
Identify what the medians actually show.
The bus sample median is one minute higher; a median does not describe every individual journey.
- 2
Check the scope of the observations.
Only six journeys per group were observed, and their values overlap.
- 3
Identify a possible alternative explanation.
The groups were not matched by journey distance, so distance or other conditions may help explain the observed difference.
- 4
Write a defensible conclusion.
In these six-person samples, the bus median was one minute longer. The groups overlap, and this evidence does not show that every bus journey is longer or that transport mode alone caused the difference.
In these six-person samples, the bus median was one minute longer. The groups overlap, and the evidence does not show that every bus journey is longer.
Try it yourself.
Check your understanding
Why state that the travel groups were not matched by distance?
Show answer & reasoning
Distance may help explain the times.
Longer journeys may take more time regardless of travel mode. Because distance was not matched, it is a possible alternative explanation, so the observed time difference cannot be attributed to transport mode alone.
Keep practising
6 worksheet questions · 14 marks
Read the questions online
- Write a precise question about Year 9 homework time, naming a population and measurement.2 marks
- Suggest a fair sample for comparing homework time in two Year 9 classes.2 marks
- For walking times 8, 10, 10, 12, 15, 17, calculate mean, median and range.3 marks
- A student records 600 minutes for a short school journey. What should happen before analysis?2 marks
- Choose a display to compare the supplied walking and bus times.2 marks
Six observations per group. Rows are not matched students. Walk (min) Bus (min) 8 5 10 8 10 12 12 12 15 15 17 20 - Give two limitations of an investigation using six volunteers from each travel group.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write a precise question about Year 9 homework time, naming a population and measurement.2 marks
Name the target group.
Define minutes and a usual school night for comparability.
For Year 9 students at this school, how many minutes of homework are completed on a usual school night? - Suggest a fair sample for comparing homework time in two Year 9 classes.2 marks
Include both groups in the frame.
Report non-response rather than silently replacing inconvenient answers.
Randomly select from both rolls, using the same question and measurement period. - For walking times 8, 10, 10, 12, 15, 17, calculate mean, median and range.3 marks
Total 72, mean .
Median ; range .
Mean 12 min; median 11 min; range 9 min. - A student records 600 minutes for a short school journey. What should happen before analysis?2 marks
An unusual value may be a mistake or a real event.
Document the decision instead of silently deleting it.
Check the source and units; correct only a confirmed error. - Choose a display to compare the supplied walking and bus times.2 marks
Six observations per group. Rows are not matched students. Walk (min) Bus (min) 8 5 10 8 10 12 12 12 15 15 17 20 Both groups measure the same numerical variable.
A common scale reveals centre, spread and overlap.
Two dot plots on the same minute scale, or a back-to-back stem-and-leaf plot. - Give two limitations of an investigation using six volunteers from each travel group.3 marks
Voluntary selection can introduce bias.
Small unmatched samples limit generalisation and causal claims.
Small samples may vary; volunteers may not represent everyone; journey distances may differ. Any two explained.
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 ↗