Scatter Graphs & CorrelationCambridge IGCSE Maths: Revision notes
Section 1
What is a scatter graph?
A scatter graph (or scatter diagram) plots pairs of values for two variables, one on each axis, to show whether a relationship exists between them. Each pair of data is plotted as a single point — on exam papers, points should be plotted as small crosses (×), not dots or circles, so the exact position is clear.
Always plot points as small, neat crosses (×) — examiners can lose marks for dots or blobs that make the exact position ambiguous.
Section 2
What is correlation?
Correlation describes the type of relationship shown by the pattern of points on a scatter graph.
| Type | Pattern | Meaning |
|---|---|---|
| Positive correlation | Points trend upward left to right | As one variable increases, so does the other |
| Negative correlation | Points trend downward left to right | As one variable increases, the other decreases |
| Zero (no) correlation | Points show no clear pattern | No linear relationship between the variables |
The closer the points are to forming a straight line, the stronger the correlation; the more scattered they are, the weaker the correlation.
Correlation shows a relationship exists, but it does not prove one variable causes the other — do not write 'causes' in an exam answer unless the question supports it.
Section 3
How do you draw a line of best fit?
A line of best fit is a single straight line drawn by eye to represent the trend of the data. To draw one correctly:
- Draw a single ruled straight line (not a curve, not a series of segments)
- The line should extend across the full range of the plotted data
- Points should be roughly evenly distributed on either side of the line — not all points above or below
- The line does not need to pass through the origin or any particular point unless the data suggests it should
The line of best fit is drawn 'by inspection' — there is no single correct line, but it must follow the overall trend fairly.
If a scatter graph shows positive correlation between hours studied and test score, the line of best fit should slope upward and have roughly equal numbers of points above and below it.
Section 4
How is a scatter graph used to make predictions?
Once a line of best fit is drawn, it can be used to estimate or predict a value:
- Find the known value on one axis
- Draw a line up/across to meet the line of best fit
- Read across/down to the other axis to estimate the corresponding value
Interpolation (estimating within the range of the plotted data) is generally reliable. Extrapolation (estimating outside the range of plotted data, beyond the line of best fit) is less reliable, because the trend may not continue.
If asked to comment on the reliability of a prediction, state clearly whether it is interpolation (reliable) or extrapolation (unreliable, as the trend beyond the data is unknown).
Must Know
- Scatter graphs plot pairs of data as points (crosses ×) to show relationships between two variables
- Positive correlation: both variables increase together
- Negative correlation: one increases as the other decreases
- Zero correlation: no clear linear pattern
- Line of best fit: one ruled straight line, drawn by eye, across the full data range, with points roughly evenly spread either side
- Interpolation (within data range) is more reliable than extrapolation (beyond data range)
That's the notes covered.
Carry on to the next subtopic.