Pictograms, bar charts, pie charts and percentage bar charts

Last time

Before we start: last time, in Statistical terms, types of data and surveys, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Pictures of data

Charts turn tables of numbers into pictures that are quick to read. This lesson covers pictograms, bar charts of several kinds, pie charts and percentage bar charts, and how to choose the right chart for a comparison.

Pictograms

A pictogram uses a symbol to stand for a number of items, shown in a key. If one symbol stands for 8 pupils, half a symbol stands for 4 and a quarter for 2. Symbols must all be the same size, so that the lengths of the rows can be compared.

Bar charts

A simple bar chart has one bar per category, with gaps between the bars and a scale starting at zero. A multiple, or dual, bar chart puts bars for two or more groups side by side, to compare each category across the groups. A sectional, or component, bar chart stacks the categories into one bar per group, so it shows each group's total and its parts.

Percentage bar charts

A percentage bar chart is a sectional bar chart in which every bar has the same length: 100 per cent. Each section shows a category's percentage of its group, so proportions can be compared even when the totals differ. But it hides the totals, so it cannot show which group is larger.

Pie charts

In a pie chart, each sector's angle is its frequency divided by the total, times 360 degrees. If 30 of 120 students walk to school, the walking sector is 30 over 120 times 360: 90 degrees. Check that the angles add up to 360 degrees.

Comparative pie charts

When two pie charts compare totals of different sizes, their areas must be in proportion to the totals. So the radii are in the ratio of the square roots of the totals: r two equals r one times the square root of T two over T one. Totals of 400 and 900, with the first radius 4 centimetres: the second radius is 4 times the square root of 2.25, which is 6 centimetres.

Choosing a chart

To compare the same category across groups, use a multiple bar chart. To compare totals and their parts, use a sectional bar chart or comparative pie charts. To compare proportions only, use a percentage bar chart, or pie charts of equal size.

Pie chart angles

A full set of pie chart angles for 120 students.

Mistakes that lose marks

Mistake one: drawing comparative pie charts with radii in the ratio of the totals, not of their square roots. Mistake two: no key on a pictogram, or symbols of different sizes. Mistake three: using a percentage bar chart to compare totals. The fix: the right chart, the right scale, and a key.

The full-marks tip

The full-marks tip: show the working for every angle and radius, and draw to the accuracy asked. When asked to choose a chart, say which comparison it makes easy.

On one card

So, on one card: charts. Keep it for revision.