Stem and leaf diagrams, multiple and composite bar charts, comparative pie charts, and choosing the right diagram.

What this dot point is asking

AQA wants you to draw and read stem and leaf diagrams, multiple, composite and comparative bar charts, and comparative pie charts, and to choose a suitable diagram for a given set of discrete or categorical data. Choosing the right diagram, and justifying it, is itself an exam skill.

Stem and leaf diagrams

The stem and leaf diagram is unusual among diagrams because it keeps the raw data, so once it is ordered you can read off the median, the quartiles, the mode and the range directly from it, none of which is possible from a grouped histogram. The leaves must be ordered (smallest to largest within each row) and a key is compulsory, because the same digits could mean $32$ or $3.2$ without it. A back-to-back stem and leaf diagram shares one central stem with leaves growing left and right, which is ideal for comparing two data sets such as boys' and girls' marks.

Multiple and composite bar charts

Use a multiple bar chart when you want to compare categories across groups (sales of three products in two shops), because the eye compares neighbouring bar heights easily. Use a composite bar chart when the breakdown of a single total matters (how a budget splits across departments), because the stacked segments show both the whole and its parts. Both need a clear key and equal bar widths.

Comparative pie charts

A comparative pie chart compares two data sets with different totals. The areas are made proportional to the totals, so the radii are scaled by the square root of the ratio of totals: if one total is $4$ times the other, its radius is $\sqrt{4} = 2$ times as large. This is because the area of a circle depends on the square of the radius (area $= \pi r^2$), so doubling the radius quadruples the area. Getting this scaling right is a common higher-tariff question, and the usual error is to scale the radius by the ratio of totals itself rather than by its square root, which exaggerates the larger chart far too much.

The same square-root principle applies to any area-based comparison: if a diagram represents quantity by area, the linear scale factor is the square root of the area scale factor. Sector angles within each pie are still found the usual way, with each category's angle equal to $\frac{\text{frequency}}{\text{total}} \times 360^\circ$ for that data set, so the two pies can have very different angles for the same category if the underlying proportions differ.

Choosing a diagram