Scatter Diagrams (Copy)
Cheat Sheet: Scatter Diagrams, Correlation, and Line of Best Fit (IGCSE Mathematics 0580 – CORE)
Topic: Drawing, Interpreting, and Using Scatter Graphs
1. Drawing a Scatter Diagram
- Plot each data point as a small cross (×) on a graph.
- Horizontal axis (x-axis): Independent variable (e.g., hours studied).
- Vertical axis (y-axis): Dependent variable (e.g., marks scored).
- Label both axes clearly with units if given.
2. Understanding Correlation
| Type of Correlation | Description | Appearance |
|---|---|---|
| Positive Correlation | As x increases, y increases | Points trend upward |
| Negative Correlation | As x increases, y decreases | Points trend downward |
| Zero Correlation | No obvious trend | Points scattered randomly |
Key Points:
- Stronger correlation = points closer to forming a straight line.
- Weaker correlation = points more spread out but still showing a trend.
3. Line of Best Fit (By Eye)
- A straight line drawn by inspection (no calculations).
- Should have roughly equal number of points above and below the line.
- Should extend across the full range of the data.
- Use a ruler for a straight and neat line.
4. Interpreting the Line of Best Fit
- Predict values inside or slightly outside the range of the data (interpolation and small extrapolation).
- The line shows the general trend between the two variables.
5. Important Tips
- Don’t force the line through every point; it’s about the overall trend.
- If there’s no clear trend, do not draw a line of best fit.
- In exam questions, describe correlation clearly (e.g., “strong positive correlation” or “weak negative correlation”).
This cheat sheet fully covers all CORE-level techniques for drawing, interpreting scatter diagrams, understanding correlation, and drawing and using a straight line of best fit.