Mathematics Standard • Year 12 • Module 5 • Lesson 1
Introduction to Bivariate Data and Scatterplots, Apply
Contextual Problem Set for Introduction to Bivariate Data and Scatterplots. Work through each self-contained problem, show your reasoning, then open the worked answers to check your method.
1. Core skill
A council compares weekly rainfall (mm) with the number of park visitors (hundreds): (0, 42), (5, 39), (10, 34), (15, 30), (20, 25), (25, 21). State the explanatory and response variables, give axis labels and describe the direction and form. 4 marks
2. Use the idea
For the park data in Q1, interpret the point (15,30). Then explain what the scatterplot alone cannot establish about rain and attendance. 3 marks
3. Check your reasoning
A second site records rainfall and visitors as (0, 30), (5, 31), (10, 29), (15, 32), (20, 30). Compare its pattern with the first site. Name one useful graphical check before comparing the strength. 3 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (4 marks)
Rainfall (mm) is the explanatory x-variable; park visitors (hundreds per week) is the response y-variable. Label the axes “Rainfall (mm)” and “Park visitors (hundreds)”. The points show a strong negative, approximately linear association: visitor numbers tend to fall as rainfall increases.
2. Use the idea (3 marks)
At 15 mm of weekly rain, the recorded attendance was 30 hundreds, or 3,000 visitors. The association alone does not prove that rain caused the lower attendance; other factors such as season, events or temperature may also matter.
3. Check your reasoning (3 marks)
The second site has little or no clear linear association, while the first has a strong negative association. Use comparable axis scales and units on both scatterplots so the visual spread is not distorted.