Mathematics Standard • Year 12 • Module 5 • Lesson 1
Introduction to Bivariate Data and Scatterplots, Master
Mastery Challenge 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 wildlife team records daily temperature x (°C) and lizard sightings y for six days: (18, 3), (20, 5), (22, 7), (24, 8), (26, 11), (28, 12). On graph paper, draw a scatterplot using temperature 18–28°C on the x-axis and sightings 0–14 on the y-axis. Then write a complete description of the pattern. 4 marks
2. Use the idea
A seventh day is recorded as (23, 40). State how you would handle this point before fitting or describing a trend. Give two plausible checks. 3 marks
3. Check your reasoning
Explain why the graph should show individual paired points rather than two separate lists of temperatures and sightings. State one conclusion the graph supports and one it does not. 3 marks
Self-check
For each problem, check that your answer includes the requested variable, units or contextual interpretation.
1. Core skill (4 marks)
Plot temperature (°C) on the horizontal axis and sightings per day on the vertical axis. The scatterplot has a strong positive, approximately linear association: warmer days in this sample tend to have more lizard sightings. The variables are temperature and daily sightings.
2. Use the idea (3 marks)
Treat (23,40) as a possible outlier and verify it before analysis. Check the original field sheet for a transcription error and confirm that “40” uses the same counting method and time period as the other days. Keep it if it is valid and explain its influence.
3. Check your reasoning (3 marks)
Each point preserves which sighting count belongs to which temperature; separate lists lose that pairing. The graph supports an observed positive association in this sample. It does not by itself prove temperature causes more sightings.