Plot and interpret scatter graphs; describe correlation; draw a line of best fit; use it to estimate values; and understand interpolation, extrapolation and the difference between correlation and causation.

What this dot point is asking

OCR reference S6 covers scatter graphs and correlation: plotting paired data, describing correlation, drawing a line of best fit, using it to make predictions, and understanding the limits of those predictions and the difference between correlation and causation. Scatter graphs are how bivariate data (two variables together) is displayed and interpreted. This content appears on every tier and is a reliable source of AO2 and AO3 marks, because it rewards clear interpretation and reasoning.

Plotting and describing correlation

A scatter graph reveals the relationship between two variables.

So height against shoe size usually shows positive correlation, while the age of a car against its value shows negative correlation. Describing correlation fully means naming the direction (positive or negative) and, ideally, the strength, and then stating what it means in context, which is the part that earns the interpretation marks.

The line of best fit

A line of best fit summarises the trend with a straight line.

A line of best fit is drawn to pass as close as possible to all the points, with roughly equal numbers above and below, and it should pass through the mean point of the data. It does not have to pass through the origin or any particular point. Once drawn, it is used to estimate: to predict the $y$-value for a given $x$, find the $x$ on the horizontal axis, go up to the line, and read across to the vertical axis (and the reverse to predict an $x$ from a $y$).

Predictions, interpolation and extrapolation

Predictions from a line of best fit have limits.

So if the data covers $1$ to $8$ hours of study, estimating the score for $5$ hours (interpolation) is reasonable, but estimating for $20$ hours (extrapolation) is unsafe, because the pattern may break down. OCR rewards noting that an out-of-range prediction is unreliable, which is a common follow-up question.

Correlation versus causation

A correlation does not prove one variable causes the other.

Two variables can be correlated without one causing the other, often because a third factor influences both. Ice cream sales and drowning incidents are correlated, but neither causes the other; hot weather drives both. OCR sets questions where a claimed causal link must be challenged, and the marks reward explaining that correlation only shows the variables change together and that a third variable, or the reverse direction, may be the real explanation.