Plotting scatter diagrams, bivariate data, identifying types and strength of correlation, and spotting outliers.

What this dot point is asking

AQA wants you to plot bivariate data on a scatter diagram, describe the type and strength of correlation shown, and identify any outliers that do not fit the pattern. Describing correlation accurately, naming both type and strength, is a small but reliable source of marks, and it sets up the line of best fit work that follows.

Plotting bivariate data

By convention the explanatory variable goes on the horizontal axis and the response variable on the vertical axis, so that the diagram reads as "how the response changes with the explanatory variable". Plotting accurately matters because the position of each point determines the trend you read and the line of best fit you later draw; a single mis-plotted point can look like an outlier.

Types of correlation

The direction of the slope alone tells you the type: upward to the right is positive, downward to the right is negative, and a shapeless cloud is no correlation. Examiners expect the type to be linked to the context, for example "positive correlation, so taller people tend to have larger shoe sizes".

Strength of correlation

The strength describes how closely the points follow a straight line. Strong correlation has points lying close to a line, so the relationship is tight and predictions are more reliable. Weak correlation has points more scattered while still showing a trend, so predictions are less reliable. Always describe both the type and the strength together, for example "strong positive correlation" or "weak negative correlation". A perfectly straight line of points would be perfect correlation, and a random scatter would be no correlation.

Outliers on a scatter diagram

An outlier on a scatter diagram is a point that lies well away from the pattern formed by the others. It may come from a measurement or recording error, or it may be a genuine but unusual case. You should note outliers because they can drag a line of best fit away from the true trend and distort any prediction or conclusion. Where an outlier is clearly an error, it is reasonable to set it aside before fitting the line, but a genuine unusual value should be kept and discussed. Unlike the numerical $1.5 \times \text{IQR}$ rule used for a single variable, an outlier on a scatter diagram is judged visually: it is a point that breaks the two-variable pattern, even if neither of its individual values would look unusual on its own.