The idea, step by step
Describe three separate features
Direction is positive when larger x-values tend to accompany larger y-values, and negative when larger x-values tend to accompany smaller y-values. Strength describes how closely points follow the pattern. Form describes whether that pattern is roughly linear or curved.
A steep line is not automatically a strong association. Points can lie tightly around a shallow line or widely around a steep line. Strength concerns scatter around the pattern, not the units or gradient.
Curves can be strong too
A scatterplot can have a strong curved association even when a single straight-line description is poor. Look at the full pattern rather than forcing every set of points into positive or negative linear language.
Describe an outlier separately. It can affect a fitted line or numerical summary, and it may point to a different condition worth investigating. A description should not become a causal claim.
A common trap
Strong means steep.
Instead: Changing axis units changes steepness without changing how tightly the points follow their pattern.
See the thinking
Describe a decreasing pattern
Describe the association between the outside-temperature index and heating-use index shown.
- The points decrease as temperature rises, so direction is negative.
- They lie close to a straight pattern, so the association is strong.
- The pattern is approximately linear.
Describe a curve
The pairs are (0, 0), (1, 1), (2, 4), (3, 9), (4, 16). Describe the pattern.
- The response increases with the explanatory value.
- The increases grow larger, so the shape is curved.
- All points lie on the quadratic pattern y=x².
Check your understanding
Points lie tightly around a decreasing straight line. Describe direction, strength and form.
Show answer
Strong negative linear association.
Decreasing gives negative; tight scatter gives strong; straight form gives linear.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Describe the association for(1, 9), (2, 7), (3, 5), (4, 3), (5, 1).2 marks
- Describe(1, 3), (2, 8), (3, 2), (4, 7), (5, 4).2 marks
- Can a curved pattern be strong? Give a reason.2 marks
- A graph changes from metres to centimetres on one axis. Does that alone strengthen the association?2 marks
- Describe the supplied study-time plot using all three features.2 marks
- A single point lies far from the main pattern. State two sensible next steps.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Describe the association for(1, 9), (2, 7), (3, 5), (4, 3), (5, 1).2 marks
Every increase of 1 in x gives a decrease of 2 in y.
All points lie on y=11−2 x.
Perfect negative linear association. - Describe(1, 3), (2, 8), (3, 2), (4, 7), (5, 4).2 marks
The responses alternate rather than consistently rise or fall.
Five points alone offer limited evidence.
No clear linear direction; the points are scattered. - Can a curved pattern be strong? Give a reason.2 marks
Strength means closeness to a pattern.
Points may lie very close to a curve.
Yes. - A graph changes from metres to centimetres on one axis. Does that alone strengthen the association?2 marks
Only the unit scale changes.
The underlying paired observations and relative pattern are unchanged.
No. - Describe the supplied study-time plot using all three features.2 marks
Scores generally rise with study time.
There is some scatter around a roughly straight trend.
Positive, quite strong, approximately linear association. - A single point lies far from the main pattern. State two sensible next steps.2 marks
An unusual point is not automatically wrong.
Report and justify any later exclusion.
Check the recording/measurement and investigate its context.
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 ↗