Scatter Plots
Correlation and Relationships in Data · Level 5
Ngā Whāinga Akoranga · Learning Intentions
- Plot data as a scatter graph and draw a line of best fit
- Identify correlation: positive, negative, or none
- Understand that correlation does NOT mean causation
- Make predictions from trend lines and evaluate their reliability
Paearu Angitu · Success Criteria
- I can correctly plot (x, y) data points on a scatter graph
- I can draw a line of best fit and use it to make a prediction
- I can classify correlation as positive, negative, or none
- I can explain why correlation ≠ causation with an example
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.
Whakataukī
"Mā te whakaaro, ka mārama"
Through reflection comes clarity.
When our tīpuna observed the natural world — stars guiding navigation, wind direction predicting rain — they understood that some things are related. Scatter plots reveal those connections in data. Not all relationships are simple, and observation requires careful thought: correlation shows a pattern, but it does not prove a cause.
Ngā Āhua Hononga · Types of Correlation
As one variable increases, the other also increases. Points slope up from left to right.
e.g. height and shoe size
As one variable increases, the other decreases. Points slope down from left to right.
e.g. speed and travel time
No clear pattern. Points are scattered randomly.
e.g. shoe size and test score
Important: Correlation ≠ Causation. Just because two things trend together does not mean one causes the other. Always ask: could something else explain both?
Kauwhata 1 · Student Height vs Shoe Size
| Height (cm) | 150 | 155 | 160 | 163 | 165 | 168 | 170 | 173 | 175 | 178 | 180 | 183 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Shoe size (NZ) | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | 10 | 10 | 11 | 12 |
1. What is the general trend you observe in this data?
2. Using your line of best fit, predict: what shoe size might a 185 cm student wear?
3. Are there any outliers — data points that don't fit the trend? Circle them on your graph. What might explain them?
Kauwhata 2 · Study Time vs Test Score
| Study time (hrs) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 5 | 5.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| Test score (%) | 42 | 48 | 55 | 58 | 62 | 65 | 70 | 72 | 78 | 80 |
1. What does this scatter plot suggest about the relationship between study time and test scores?
2. If a student studies for 4.5 hours, what score might they achieve? How confident are you in this prediction?
3. CRITICAL THINKING: Does studying MORE always guarantee a HIGHER score? What other factors might matter?
Kauwhata 3 · Design Your Own Investigation
Choose two variables you think might be related. Collect data from at least 10 classmates.
My two variables: X = __________________________ Y = __________________________
My hypothesis — what correlation do I predict? (circle one) Positive Negative None
Why do I expect this?
| Participant | X value | Y value | Participant | X value | Y value |
|---|---|---|---|---|---|
| 1 | 6 | ||||
| 2 | 7 | ||||
| 3 | 8 | ||||
| 4 | 9 | ||||
| 5 | 10 |
What correlation did you find? Was it what you predicted? What might explain any differences?
Give one reason why your result might NOT show causation even if correlation exists.
Aronga Mātauranga Māori
Traditional Māori knowledge systems are built on careful observation of correlations in the natural world: the flowering of mānuka correlates with the arrival of whitebait, the call of the kōkako correlates with rain, the position of Matariki correlates with optimal planting times. This is correlational knowledge built over generations — and Māori scientists today integrate these patterns with quantitative data to understand environmental change.
The critical distinction — correlation vs causation — is also present in te ao Māori. Tohu (signs) indicate patterns without necessarily causing them. A Maramataka practitioner reads tohu as correlated signals; the question of mechanism (why do they correlate?) requires deeper investigation. The same intellectual humility applies in modern statistical reasoning.
Ngā Rauemi Tautoko · Support Materials
Resources already provided:
- This handout with data tables and scatter graph grids
- Ruler — for drawing the line of best fit as a straight line
- Calculator (permitted throughout)
- Graph paper (optional backup if grid boxes are too small)
Aronga Rerekē · Differentiated Pathways
Tīmata · Entry Level
Complete Scatter Graph 1 only. Plot the points, draw the line of best fit with a ruler, and answer questions 1 and 2.
Paerewa · On Level
Complete Scatter Graphs 1 and 2. Answer all questions including the critical thinking question. Begin your own investigation.
Tūāpae · Extension
Complete all three graphs. For your own investigation, calculate the mean point (x̄, ȳ) and verify your line of best fit passes through it. Find a real-world example of a misleading correlation (spurious correlation) and explain why it does not imply causation.