Understand the idea.
Plan before collecting
A fair investigation begins with a precise question, target group and measurement rule. For travel times, define one-way or return travel, the relevant day and units in minutes. Different interpretations of the same question can create differences that are only measurement inconsistencies.
Plan the selection method, neutral wording and treatment of missing or unclear answers before collecting. Use a frame that covers the target group and ask only for information needed to answer the question. Clear rules help another investigator repeat the collection.
Analyse the whole story
Check the records, select an appropriate display, and calculate summaries that address the question. Compare centre and spread rather than reporting only one average. Retain valid unusual observations and explain their effect; correct only genuine errors supported by the records.
Finish by interpreting results in context and stating limitations in coverage, response, size or timing. Suggest a specific improvement for the next collection. A graph presents information, but the investigation also needs a supported conclusion and an honest account of uncertainty.
| Code | Minutes |
|---|---|
| A | 5 |
| B | 10 |
| C | 10 |
| D | 15 |
| E | 15 |
| F | 15 |
| G | 20 |
| H | 30 |
See the method in action.
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 |
Worked solution
- 1
Check the ordered observations and mean.
All eight sampled students contribute one one-way journey time.
- 2
Average the two middle values.
With eight ordered observations, positions four and five determine the median.
- 3
Find the most frequent observation.
Fifteen minutes occurs three times, more often than any other time.
- 4
Report the range alongside the centre.
Equal mean, median and mode do not remove the substantial variation between individual journeys.
Mean, median and mode 15 minutes; range 25 minutes.
Worked example 2
A study of all Year 8 travel times asks only students at a bus stop. Improve the plan.
Worked solution
- 1
Identify the coverage problem.
A bus-stop frame favours bus travellers and misses Year 8 students who walk, cycle or travel by other routes.
- 2
Use a frame covering the whole target group.
Select fairly from a complete Year 8 roll so all eligible students have a chance of inclusion.
- 3
Standardise what each student reports.
Ask everyone for one-way journey time in minutes for the same defined day or period, so the responses measure the same variable.
- 4
Report the remaining limitations.
Record sample size and missing responses, then describe what the sample supports without assuming it includes every Year 8 student.
Use the whole-year frame, not just the bus stop.
Try it yourself.
Check your understanding
Why is “everyone takes 15 minutes” not justified by the supplied data?
Show answer & reasoning
Times vary from 5 to 30 minutes and only eight students were sampled.
Fifteen minutes is the sample's mean, not every student's journey. The eight observations range from 5 to 30 minutes, and those sampled students do not establish every population member's time.
Keep practising
6 worksheet questions · 14 marks
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 .
.
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 .
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 ↗