Scatter Diagrams and Correlation
A scatter diagram shows whether two variables are related. The mathematics is light — the marks are for describing the correlation properly and for drawing a sensible line of best fit.
1. Plotting
Each point is a pair of values (x, y) for one item — one person’s height and mass, say.
Read the coordinates carefully and check both scales, which are often different on each axis. Careless plotting was a recorded error and everything after it goes wrong.
Mark points with a small, neat × or dot.
2. Types of correlation
| Correlation | Pattern | Meaning |
|---|---|---|
| Positive | points rise left to right | as one increases, the other increases |
| Negative | points fall left to right | as one increases, the other decreases |
| No correlation | scattered, no pattern | no relationship |
Strength: the closer the points are to a straight line, the stronger the correlation.
Describe correlation with TWO words: strength and type. “Strong positive correlation”, “weak negative correlation”. A one-word answer typically scores half.
Then say what it means in context. “There is a strong positive correlation, so students who spent longer revising generally scored higher marks.” The context sentence is usually a separate mark.
Positive correlation is not the same as direct proportion. Direct proportion means a straight line through the origin with a constant ratio; positive correlation just means an upward trend. Confusing them was specifically recorded.
3. Line of best fit
A straight line following the general trend, with roughly equal numbers of points on each side.
Rules:
- Use a ruler
- Follow the overall trend
- Aim for a balance of points above and below
- It does not have to pass through any of the points
- It should pass through the mean point (mean x, mean y) if you know it
- Ignore outliers when positioning it
A line of best fit does not join the highest points, and it is not a curve through every point. Thinking it should touch the extremes was a documented error — it is a summary of the trend, deliberately not passing through everything.
Don’t force it through the origin unless the data genuinely supports that.
Only draw one if there IS correlation. If the points show no pattern, a line of best fit is meaningless.
4. Using the line
Read across and down (or up) from the known value to estimate the other.
Interpolation — estimating inside the range of the data. This is reliable.
Extrapolation — estimating outside the range. This is unreliable, because the trend may not continue.
If asked to comment on the reliability of an estimate, check whether it is inside or outside the data range. An estimate beyond the plotted values should be described as unreliable, and saying why earns the mark.
Show your reading lines on the diagram — examiners look for them.
5. Outliers
An outlier is a point that clearly does not fit the pattern.
- Identify it (circle it and give its coordinates)
- Ignore it when drawing the line of best fit
- It may be a measurement or recording error
6. Correlation is not causation
Correlation shows that two variables are RELATED. It does not prove one CAUSES the other.
Ice-cream sales and sunburn cases correlate strongly, but ice cream does not cause sunburn — hot weather drives both.
Never write “X causes Y” from a scatter diagram. Say the variables are associated, or that as one increases the other tends to increase. This distinction is examined directly.
7. Scope note
Some lessons used the calculator’s STAT mode to compute a regression line.
Regression is not required on 0580 — you are expected to draw a line of best fit by eye with a ruler. The calculator method is fine as a check, but the drawn line is what earns marks. Check your own syllabus document.
8. Mistakes that cost marks
Plotting inaccurately or misreading the scales.
Describing correlation with one word instead of strength and type.
Not interpreting the correlation in context.
Confusing positive correlation with direct proportion.
Drawing a line of best fit through the extreme points.
Drawing a curve or a freehand line.
Including an outlier when positioning the line.
Drawing a line when there is no correlation.
Treating extrapolation as reliable.
Claiming causation.
Frequently asked questions
What is positive correlation? As one variable increases, so does the other — the points rise from left to right.
What is negative correlation? As one increases, the other decreases — the points fall from left to right.
How do I describe correlation? Give strength and type — e.g. “strong negative correlation” — then explain what it means in context.
What is a line of best fit? A straight line following the trend, with roughly equal points on either side.
Does it have to pass through the origin? No — only if the data supports it.
What is interpolation? Estimating within the data range — reliable.
What is extrapolation? Estimating outside the range — unreliable, as the trend may not continue.
What is an outlier? A point that doesn’t fit the pattern; ignore it when drawing the line.
Does correlation prove causation? No. It shows a relationship only.
Quick revision checklist
- I plot points accurately, checking both scales
- I can identify positive, negative and no correlation
- I describe correlation with strength and type
- I interpret the correlation in context
- I know correlation isn’t direct proportion
- I draw a line of best fit with a ruler, balancing the points
- I don’t force it through the origin or the extremes
- I ignore outliers when drawing it
- I can use the line to estimate, showing my reading lines
- I know interpolation is reliable and extrapolation is not
- I can identify and comment on an outlier
- I never claim causation
These notes cover scatter diagrams and correlation in the Cambridge IGCSE Mathematics (0580) syllabus, and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Maths lessons. This was the least-covered topic in that set, so the page follows the syllabus closely and is deliberately concise rather than padded. Always check the current syllabus for your own exam series.
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