Mathematics Standard • Year 12 • Module 5 • Lesson 2
Describing Correlation, Build
Scaffolded Practice for Describing Correlation. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
Classify each described scatterplot by direction and strength. (a) Points lie close to an upward-sloping line. (b) Points are widely scattered but tend to slope down. (c) Points form a roughly circular cloud with no trend. 3 marks
2. Use the idea
For the study-time data (1,52), (2,57), (3,59), (4,63), (5,68), (6,70), write one complete sentence describing the correlation. Include both variables. 2 marks
3. Check your reasoning
A scatterplot curves upward: y rises slowly at first and then rapidly as x increases. Why is “strong positive linear correlation” not a complete description? 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
(a) Strong positive linear correlation. (b) Weak negative linear correlation. (c) No clear linear correlation. Strength describes how closely the points follow a pattern; direction describes whether the trend rises or falls.
2. Use the idea (2 marks)
There is a strong positive, approximately linear correlation between study time and test score for these students: students who studied longer tended to score higher.
3. Check your reasoning (2 marks)
The direction is positive and the pattern may be strong, but its form is curved rather than linear. A complete description should say strong positive, nonlinear (curved) association.