Bar Charts, Pie Charts and Pictograms

This lesson covers the main types of statistical diagrams you need to draw and interpret for AQA GCSE Mathematics. Being able to read information from charts, draw them accurately, and spot misleading representations are all important skills that will be tested in the exam.

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Bar Charts

A bar chart uses rectangular bars to represent data. The height (or length) of each bar shows the frequency.

Key Features of a Bar Chart

• The bars must be the same width.
• There must be equal gaps between the bars (for categorical or discrete data).
• The axes must be labelled clearly.
• The chart should have a title.
• The frequency axis must start at zero and use a consistent scale.

Types of Bar Chart

Type	Description	When to Use
Simple bar chart	One bar per category	Showing frequencies for a single data set
Dual (comparative) bar chart	Two bars side by side for each category	Comparing two data sets
Composite (stacked) bar chart	Bars are stacked on top of each other	Showing how a total is split into parts

Reading a Bar Chart

When reading values from a bar chart:

1. Identify which axis shows the categories and which shows the frequency.
2. Read the height of the bar carefully using the scale.
3. Check whether the scale starts at zero — if not, the chart may be misleading.

Exam Tip: If asked to draw a bar chart, use a ruler and make sure all bars are the same width. Uneven bars or missing labels will cost you marks. Always include a title, axis labels, and a consistent scale.

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Dual Bar Charts

A dual bar chart (also called a comparative bar chart) shows two sets of data side by side for each category, usually in different colours or patterns.

Worked Example

The number of boys and girls who achieved each grade in a test:

Grade	Boys	Girls
A	5	8
B	12	10
C	15	14
D	8	6

In a dual bar chart, each grade would have two bars next to each other — one for boys and one for girls. A key must be included to show which colour represents which group.

From this chart you can directly compare how many boys and girls achieved each grade.

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Composite (Stacked) Bar Charts

A composite bar chart stacks the bars on top of each other. The total height of the bar shows the overall total, and each section shows the contribution of each category.

Using the same data:

Grade	Boys	Girls	Total
A	5	8	13
B	12	10	22
C	15	14	29
D	8	6	14

Each bar would have a boys section (bottom) and a girls section (top). The total height of each bar shows the combined total.

Exam Tip: In a composite bar chart, to find the frequency of the top section, you must subtract the bottom section from the total height. Do not simply read the top of each coloured section as if it starts from zero.

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Pie Charts

A pie chart is a circle divided into sectors, where each sector represents a proportion of the whole. The angle of each sector is proportional to the frequency.

Drawing a Pie Chart

To calculate the angle for each sector:

Angle = (frequency / total frequency) x 360

Worked Example

40 students were asked about their favourite colour.

Colour	Frequency	Angle
Red	12	(12/40) x 360 = 108 degrees
Blue	15	(15/40) x 360 = 135 degrees
Green	8	(8/40) x 360 = 72 degrees
Yellow	5	(5/40) x 360 = 45 degrees
Total	40	360 degrees

Always check: the angles must add up to 360 degrees.

To draw the pie chart:

1. Draw a circle using a compass.
2. Draw a radius (a line from the centre to the edge).
3. Use a protractor to measure each angle from the previous line.
4. Label each sector clearly.

Reading a Pie Chart

To find the frequency from a pie chart:

Frequency = (angle / 360) x total

Worked Example

A pie chart shows the favourite sports of 90 students. The sector for football has an angle of 140 degrees.

Number who chose football = (140/360) x 90 = 35 students

Exam Tip: In pie chart questions, always show the calculation for each angle. If the angles do not add up to exactly 360 degrees, you have made an error. In the exam, measure and draw angles using a protractor — accuracy within 2 degrees is expected.

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Pictograms

A pictogram uses symbols (pictures) to represent data. Each symbol represents a specific number of items, shown in a key.

Key Rules for Pictograms

• A key must be included (e.g. each symbol = 4 people).
• Symbols must be the same size.
• Part-symbols can be used to show fractions of the value (e.g. half a symbol = half the value).

Worked Example

A pictogram shows the number of ice creams sold each day. The key states: each symbol = 10 ice creams.

Day	Symbols	Number Sold
Monday	3 full symbols	30
Tuesday	4 full symbols, half symbol	45
Wednesday	2 full symbols	20
Thursday	5 full symbols, quarter symbol	52 (approximately)

Limitations of Pictograms

• They are not very precise — it can be hard to read part-symbols accurately.
• They are only suitable for simple data with small frequencies.
• Different people may interpret part-symbols differently.

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Misleading Graphs

Graphs can be drawn in ways that mislead the reader. Common tricks include: