The idea, step by step
Plan before collecting
Choose a population and a question involving two variables measured on each individual. Define exactly how each variable is recorded, including units and precision. Decide how to sample and avoid collecting unnecessary identifying information.
Predict practical sources of error and confounding. A plan about study time and test score needs a consistent definition of study time and comparable tests; otherwise the pairings may mix unlike quantities.
Analyse, conclude and qualify
Use an appropriate scatterplot for two numerical variables or conditional percentages for two categorical variables. Describe the pattern with numerical or graphical evidence, and look for unusual observations. Keep the raw data so someone can check the analysis.
State the sample size, selection method and limitations. Distinguish association from causation and interpolation from extrapolation. A useful investigation may end with a cautious conclusion and a specific suggestion for improving the study.
A common trap
A good investigation must prove the prediction.
Instead: A good investigation answers fairly. Unexpected or inconclusive evidence is still a legitimate result.
See the thinking
A complete small numerical analysis
Six volunteers report weekly revision hours and a common quiz score. Analyse the supplied pairs.
| Revision(h/week) | Quiz score/100 |
|---|---|
| 1 | 40 |
| 2 | 50 |
| 3 | 60 |
| 4 | 65 |
| 5 | 80 |
| 6 | 85 |
- The sample is 6 volunteers, so selection limits generalisation.
- Plot the paired observations; the pattern rises roughly linearly.
- State a positive association in these data, not proof that extra revision alone caused the scores.
Improve a measurement plan
A group wants to compare arm span with height. They use different units and some wear shoes. Improve the plan.
- Use the same unit, such as centimetres, for both measurements.
- Measure height without shoes using a consistent technique.
- Record each person's height and arm span on the same row and use a fair sample.
Check your understanding
Why must both measurements be recorded on the same row?
Show answer
To preserve which two values belong to the same individual.
The scatterplot uses paired observations, not independent lists.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Write a focused bivariate question about students that uses two numerical variables.2 marks
- State a consistent recording plan for height and arm span.2 marks
- Why might choosing only the basketball team limit a height/arm-span investigation about all Year 10 students?2 marks
- Describe the supplied revision/score pattern and one limitation.3 marks
- Give one reason not to predict the score for 20 revision hours from data covering 1–6 hours.2 marks
- A class finds no clear pattern. Write an honest conclusion and one improvement.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write a focused bivariate question about students that uses two numerical variables.2 marks
Specify a population.
Choose two measurable numerical variables.
For example:'Among Year 10 students, is height associated with arm span?' - State a consistent recording plan for height and arm span.2 marks
Use common units and precision.
Keep pairs together.
Measure both in centimetres with the same procedures; record paired values for each participant. - Why might choosing only the basketball team limit a height/arm-span investigation about all Year 10 students?2 marks
Team selection can relate to physical characteristics.
Use a wider sampling frame.
The selected group may not represent the full year. - Describe the supplied revision/score pattern and one limitation.3 marks
Scores tend to rise with reported revision hours.
Self-reporting and confounding also limit interpretation.
Positive roughly linear association; the small volunteer sample may be unrepresentative. - Give one reason not to predict the score for 20 revision hours from data covering 1–6 hours.2 marks
The relationship may not continue unchanged.
The sample does not support that range.
It is extrapolation far beyond the observed range. - A class finds no clear pattern. Write an honest conclusion and one improvement.3 marks
Do not change or hide data to support the prediction.
Improve a specific limitation rather than promise a different result.
No clear association was found in this sample; collect a larger, fairer sample with more consistent measurements.
Curriculum reference & lesson scope
Australian Curriculum v 9 and SA Curriculum Mathematics
Year 10 continuous distributions, bivariate data, two-way categorical tables, bias and investigations, with the approved percentile and standard-deviation content included in the normal chapter.
Official curriculum source ↗