What you'll learn
Scatter diagrams show whether two quantities are related, and they are part of the Statistics section of the CSEC Mathematics syllabus. By plotting pairs of values as points, you can see at a glance whether — for example — taller students tend to have larger shoe sizes, or whether revision time relates to exam marks. In this guide you will learn how to draw a scatter diagram, how to describe the correlation it shows, how to draw and use a line of best fit, and how to make predictions from it. You will also learn the important caution that correlation does not prove causation. These skills appear in Paper 1 and Paper 2 and connect to data handling and interpretation.
Key terms and definitions
Scatter diagram (scatter graph) — a graph of plotted points, each representing a pair of values for two variables.
Correlation — the relationship or tendency between two variables.
Positive correlation — as one variable increases, the other tends to increase.
Negative correlation — as one variable increases, the other tends to decrease.
Line of best fit — a straight line drawn through the points to show the trend.
Outlier — a point that lies far from the general pattern.
Causation — one variable actually causing a change in the other (distinct from correlation).
Core concepts
Plotting a scatter diagram
Each item provides a pair of values, say (x, y), which is plotted as a single point. One variable goes on the horizontal axis and the other on the vertical axis, each with a suitable scale. The resulting cloud of points reveals whether the variables move together, move oppositely, or show no clear relationship.
Describing correlation
The pattern of points describes the correlation. Positive correlation: points rise from lower-left to upper-right (both increase together), e.g. height and arm span. Negative correlation: points fall from upper-left to lower-right (one increases as the other decreases), e.g. speed and journey time. No correlation: points are scattered with no trend. Correlation can also be described by strength — strong (points close to a line) or weak (points loosely scattered).
The line of best fit
When there is correlation, you can draw a single straight line that best represents the trend. A good line of best fit passes through the middle of the points, with roughly as many points above as below, and ideally passes through the mean point (the average of all x-values, average of all y-values). It does not need to touch any actual points and should not be forced through the origin.
Using the line to predict
Once drawn, the line of best fit lets you estimate a value: read up from a given x-value to the line, then across to the y-axis (or vice versa). Predictions are most reliable within the range of the data (interpolation). Predicting far beyond the data (extrapolation) is unreliable, because the pattern may not continue.
Outliers
An outlier is a point that does not fit the general pattern. It may come from a measurement error or a genuinely unusual case. Outliers should be noted and usually excluded when drawing the line of best fit, since they can pull it away from the true trend.
Correlation versus causation
A strong correlation shows that two variables tend to change together, but it does not prove that one causes the other. Both might be influenced by a third factor, or the link could be coincidental. CSEC expects you to recognise this distinction and avoid claiming causation from correlation alone.
Worked examples
Example 1: Describing correlation (Paper 1 style)
A scatter diagram of "hours of revision" against "exam mark" shows points rising from lower-left to upper-right, fairly close to a line. Describe the correlation.
The points rise together and lie close to a straight line, so this is strong positive correlation: more revision is associated with higher marks.
Example 2: Using a line of best fit (Paper 2 style)
A line of best fit for "temperature (°C)" against "cold drinks sold" passes through (20, 50) and (30, 90). Estimate the sales when the temperature is 25 °C.
The line rises by 40 (from 50 to 90) as temperature rises by 10 (from 20 to 30), a gradient of 4 drinks per °C. At 25 °C, sales ≈ 50 + 4 × (25 − 20) = 50 + 20 = 70 drinks.
Example 3: Recognising the limits (Paper 2 style)
Using the same line, a student predicts sales at 45 °C. Comment on the reliability.
45 °C is well beyond the data range used to draw the line, so this is extrapolation and is unreliable — the relationship may not continue at extreme temperatures, and such a temperature may be outside normal conditions.
Common mistakes and how to avoid them
Joining the points dot-to-dot. A scatter diagram is not a line graph; never connect consecutive points. Draw a single line of best fit instead.
Forcing the line through the origin. The line of best fit should follow the data, not be made to start at (0, 0) unless the data supports it.
Letting an outlier distort the line. Identify outliers and ignore them when positioning the line of best fit.
Claiming causation. Correlation alone does not prove that one variable causes the other; state this when asked to interpret.
Extrapolating too far. Predictions outside the data range are unreliable; keep estimates within the plotted range.
Exam technique for Scatter Diagrams
Plot carefully with a sensible scale. Use the full grid so the pattern is clear, and label both axes with units.
Describe correlation in two parts. State the direction (positive/negative/none) and the strength (strong/weak).
Balance the line of best fit. Aim for roughly equal numbers of points above and below, passing through the mean point.
Predict by reading off the line, and say whether your prediction is interpolation (reliable) or extrapolation (unreliable).
Mention causation carefully. If asked whether one causes the other, explain that correlation does not establish cause.
Quick revision summary
A scatter diagram plots pairs of values as points to reveal the relationship between two variables. Positive correlation shows points rising together; negative correlation shows one rising as the other falls; no correlation shows a random scatter — and the relationship can be strong (points near a line) or weak. When correlation exists, draw a line of best fit through the middle of the points, balanced with about as many above as below and passing through the mean point; do not join the points dot-to-dot or force the line through the origin. Use the line to predict by reading off values, trusting estimates within the data range (interpolation) far more than those beyond it (extrapolation). Treat outliers with care and exclude them from the line. Crucially, remember that correlation does not prove causation — two variables can move together without one causing the other.