Scatter Diagrams
Year 9 📈 Statistics & Probability Plot scatter diagrams, describe correlation, draw lines of best fit.
📊 Drawing and Reading Scatter Diagrams
A scatter diagram plots two variables against each other to investigate a relationship — called correlation.
- Positive correlation: as $x$ increases, $y$ increases
- Negative correlation: as $x$ increases, $y$ decreases
- No correlation: points are scattered with no clear pattern
Always describe correlation as strong or weak as well as positive or negative.
📈 Line of Best Fit
A line of best fit models the relationship and is used to make predictions.
- Draw the line so roughly equal numbers of points are above and below it.
- The line should pass through (or near) the mean point $(\bar{x}, \bar{y})$.
- Use the line to predict values: interpolation (within data range) is more reliable than extrapolation (outside range).
Extrapolation is unreliable because the relationship may not continue outside the data range.
⚠️ Correlation is Not Causation
Two variables may appear related simply because both depend on a third variable.
Classic example: Ice cream sales and drowning rates both increase in summer — but eating ice cream does not cause drowning. The third variable is hot weather.
Always ask: could a third variable (a lurking variable) explain the correlation?
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Scatter Diagrams
📊 Scatter Plot Tool
Enter x and y data to find the correlation coefficient (PMCC).