Designing and reporting an investigation | Year 9

01 / LEARN

The idea, step by step

Plan before collecting

Define the population, variable and comparison. For example: Among our Year 9 students, how do one-way school journey times compare for walkers and bus travellers? Decide what a usual school morning means, record minutes, and plan how to handle unusual delays before seeing the results.

Sample fairly from both travel groups. Use the same wording and measurement period, and record response rates. Collect only information needed for the question; anonymous codes are usually enough. Obtain suitable permission before collecting personal information.

Analyse and review

Check units, impossible values, missing observations and recording mistakes. Document justified corrections. Make a suitable display and calculate centre and spread. The conclusion must answer the original question with numerical evidence rather than just list calculations.

State limits. Travel distance might differ between groups, so an observational comparison does not establish that transport mode causes a difference. A larger fair sample, or comparison among students travelling similar distances, could improve the investigation.

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

A common trap

An investigation is complete after calculating a mean.

Instead: Answer the question, explain the method, consider variation and acknowledge limitations.

02 / WORKED EXAMPLES

See the thinking

Example 1

Compare journey times

Use the supplied walking and bus times to compare the samples.

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 totals are 72, giving mean $72 / 6 = 12$ minutes.
Walking median $= (10 + 12) / 2 = 11$ , range $= 17 - 8 = 9$ .
Bus median $= (12 + 12) / 2 = 12$ , range $= 20 - 5 = 15$ . The groups overlap.

Both means 12; walking median 11/range 9; bus median 12/range 15.

Example 2

Improve a conclusion

A report says: Bus travel is always slower because its sample median is 12 rather than 11. Improve it.

Describe these samples, not every journey.
Include small sample sizes, overlap and variation.
Distance may differ, and no causal claim has been established.

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.

Check your understanding

Why state that the travel groups were not matched by distance?

Show answer

Distance may help explain the times.

Without accounting for distance, transport mode alone is not an established cause.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

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 $72 / 6 = 12$ .
Median $(10 + 12) / 2 = 11$ ; range $17 - 8 = 9$ .
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.

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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 ↗

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