Mathematics Standard • Year 12 • Module 5 • Lesson 2
Describing Correlation, Master
Mastery Challenge for Describing Correlation. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
Three studies report these patterns: A, tight upward line; B, loose downward cloud; C, tight U-shape. For each, state direction and strength, and identify whether a linear description is suitable. 4 marks
2. Use the idea
For a dataset on age of a car and resale value, the points follow a tight downward-sloping line. Write a full contextual description and state one limitation of that sentence. 3 marks
3. Check your reasoning
Explain why “the correlation is negative” is incomplete when asked to describe a scatterplot. List the other features a full response should consider. 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (4 marks)
A: strong positive, linear. B: weak negative, approximately linear. C: strong curved/nonlinear pattern with no single direction across the full range, so a linear description is unsuitable.
2. Use the idea (3 marks)
There is a strong negative, approximately linear correlation between car age and resale value: older cars in the sample tend to have lower resale values. The statement describes association in the sample; it does not establish causation or guarantee an individual car’s value.
3. Check your reasoning (2 marks)
It gives direction only. A complete description should also state strength, form (linear or curved), and name the variables in context; mention unusual points if relevant.