Mathematics Standard • Year 12 • Module 5 • Lesson 2
Describing Correlation, Apply
Contextual Problem Set for Describing Correlation. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A sports scientist compares weekly training hours and sprint time. The points form a tight downward-sloping band. Describe direction, strength and likely form, then interpret the result without claiming causation. 3 marks
2. Use the idea
Another scatterplot of shoe size and reading score is a broad cloud with no visible upward or downward trend. State what can be concluded about linear correlation, and avoid overclaiming. 3 marks
3. Check your reasoning
A scatterplot has a clear upward curve. A student writes “moderate positive linear correlation”. Correct the description and identify which part of the student’s statement may still be useful. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
There is a strong negative, approximately linear association between training hours and sprint time: athletes with more training hours tend to have lower (faster) times. The observational pattern alone does not establish that training caused the difference.
2. Use the idea (3 marks)
There is little or no apparent linear correlation in the displayed data. This does not prove that the variables are independent in every population or rule out a curved pattern; it describes the observed scatterplot only.
3. Check your reasoning (2 marks)
Replace “linear” with “nonlinear (curved)”. “Positive” remains appropriate because y generally increases as x increases; “moderate” may describe strength if that matches how closely the points follow the curve.