Mathematics Standard • Year 12 • Module 5 • Lesson 1
Introduction to Bivariate Data and Scatterplots, Build
Scaffolded Practice 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 class records study time and test score for six students: (1, 52), (2, 57), (3, 59), (4, 63), (5, 68), (6, 70). Let x be study time in hours and y be test score out of 100. Name the explanatory and response variables, list the six points in plotting order, and state suitable axis labels. 3 marks
2. Use the idea
Using the same data in Q1, describe the overall direction and form of the association. Identify one plotted point and interpret it in context. 3 marks
3. Check your reasoning
A scatterplot has most points between x=2 and x=8 and y=10 and y=20, plus one point at (15, 48). What feature should you check before describing the overall pattern, and why? 2 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (3 marks)
The explanatory variable is study time (hours), so it goes on the horizontal x-axis. The response variable is test score (marks out of 100), so it goes on the vertical y-axis. Plot (1,52), (2,57), (3,59), (4,63), (5,68), (6,70).
2. Use the idea (3 marks)
The points show a positive, approximately linear association: higher study times tend to occur with higher scores. For example, (4,63) represents a student who studied 4 hours and scored 63 marks. This describes an association, not a guaranteed score for every student.
3. Check your reasoning (2 marks)
Check the point (15,48) as a possible outlier. It lies well away from the main cluster and may strongly affect a summary or fitted line; first verify that it is a valid observation rather than a recording error.