Bar charts
A bar chart shows the frequency of each category as a separate bar. It is the natural choice for categorical data, such as favourite sport or eye colour, where the groups are labels rather than numbers.
- Bar chart
- A chart where the height (or length) of each bar shows the frequency of a category. The bars are separated by gaps.
- Frequency
- The number of times a value or category occurs in the data.
Key rules: leave equal gaps between the bars, make every bar the same width, label both axes, and give the chart a title. The frequency axis must start at zero, otherwise the bars mislead the reader about relative size.
Gaps matter
Bar charts have gaps between the bars because the categories are separate. Frequency diagrams for grouped numerical data have bars that touch, because the values run continuously. Mixing these up is an easy mark to lose.
Pie charts
A pie chart shows how a total splits into parts, using slices of a circle. Each category gets a slice whose angle is proportional to its frequency. Because a full circle is \(360^\circ\), you share those degrees out in the same ratio as the data.
30 students named a favourite sport: Football 12, Netball 9, Swimming 6, Other 3. Find the pie chart angle for each.
Where this is assessed
Working out sector angles correctly is Criterion A (knowing the method) and Criterion D (applying it to a real data set). Drawing the chart accurately with a protractor, labelling every sector, and checking the angles sum to \(360^\circ\) is Criterion C communication.
Frequency diagrams
A frequency diagram shows numerical data grouped into equal classes, with a bar for each class. Because the data is continuous, the bars touch with no gaps between them. This is how you display something like heights or times, where the values form a continuous scale rather than separate labels.
For example, times could be grouped as \(0 \le t < 10\), \(10 \le t < 20\), and so on, with the height of each bar showing how many values fell in that class. The shape of the diagram reveals the pattern at a glance: where the data clusters, and whether it is spread evenly or bunched to one side.
Keep the classes equal
For a standard frequency diagram, use equal class widths so bar heights can be compared fairly. Unequal widths need a more careful approach that adjusts for the class size, which is beyond what this diagram assumes.
Choosing the right chart
The right chart depends on what the data is and what you want the reader to see.
- Bar chart: best for comparing the frequencies of separate categories, such as favourite subjects.
- Pie chart: best for showing how a whole splits into parts, so the reader sees each slice as a fraction of the total. It works well with only a few categories.
- Frequency diagram: best for showing the shape of grouped numerical data, such as the distribution of test times.
A quick test: if you care about the proportion each group takes of the whole, reach for a pie chart; if you care about direct comparison of amounts, reach for a bar chart.
Check yourself
Work each one through before opening the answer.
1. In a survey of 40 people, 10 chose tea. What angle would the tea sector take on a pie chart? +
Angle \(= \dfrac{\text{frequency}}{\text{total}} \times 360^\circ = \dfrac{10}{40} \times 360^\circ = \dfrac{1}{4} \times 360^\circ = \) \(90^\circ\).
2. You want to compare how many students chose each of five favourite colours. Which chart is most suitable, and why? +
A bar chart. Favourite colour is categorical data, and a bar chart lets the reader compare the frequency of each colour directly by comparing bar heights. The gaps between bars show the categories are separate.
3. On a pie chart of 60 people, one sector measures \(60^\circ\). How many people does it represent? +
The sector is \(\dfrac{60^\circ}{360^\circ} = \dfrac{1}{6}\) of the circle, so it represents \(\dfrac{1}{6} \times 60 = \) 10 people.
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