Scatter graphs, correlation and causation
WJEC examines scatter graphs every Unit 2 paper at Foundation and Intermediate. Higher candidates also need the line-of-best-fit prediction skill.
What is a scatter graph?
A plot of paired (x, y) data points — one axis per variable. Used to investigate whether two variables are related.
Types of correlation
| Correlation | Meaning | Visual cue |
|---|---|---|
| Strong positive | y rises as x rises; points cluster tightly | Tight band sloping up |
| Weak positive | upward trend but loose | Loose upward scatter |
| Strong negative | y falls as x rises; tight | Tight band sloping down |
| Weak negative | downward trend but loose | Loose downward scatter |
| No correlation | no clear pattern | Random scatter |
WJEC standard wording always wants TWO descriptors — the strength (strong/weak) AND the direction (positive/negative).
Line of best fit
A straight line drawn so that points are roughly evenly distributed above and below. By eye, not regression. Three rules:
- Don't force the line through the origin.
- Don't connect first and last points.
- Aim for roughly equal numbers of points either side.
Use the line of best fit to predict y from a given x — read horizontally to the line, then vertically down to the x-axis (or vice versa).
Interpolation vs extrapolation
- Interpolation — predicting WITHIN the data range. Generally reliable.
- Extrapolation — predicting OUTSIDE the data range. Unreliable; the relationship may not continue. WJEC awards a B1 for stating "this is extrapolation, so the prediction is unreliable".
Correlation does NOT imply causation
A correlation between ice cream sales and drowning rates exists — both rise in summer. Hot weather is the lurking variable. WJEC wording: "correlation does not mean one variable causes the other; there may be a third (lurking) factor."
Outliers
A point clearly away from the trend. Should usually be ignored when drawing the line of best fit. State "the outlier (x, y) was ignored because it lies far from the trend".
WJEC exam tip
When asked to describe correlation, always use BOTH a strength word and a direction word ("strong positive", "weak negative"). One word alone loses the A1.
AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves