Interpreting pie charts Revision Notes for Edexcel GCSE Statistics

Interpreting pie charts

What are pie charts?

Pie charts are a visual way of displaying qualitative data - information that can be categorised rather than measured numerically. They're particularly useful for showing how different categories compare to each other as parts of a whole.

The most important thing to remember about pie charts is that the angle of each sector is directly proportional to the value it represents. This means that larger values get bigger slices of the pie, and smaller values get smaller slices.

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Pie charts work best when you have categorical data that makes up parts of a meaningful whole. They're less effective when categories don't relate to each other or when you have too many small categories.

The key principle

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Since a complete circle contains 360°, all the angles in a pie chart must add up to exactly 360°. This is your first check when interpreting or creating pie charts - if the angles don't total 360°, something has gone wrong!

The essential formula

To work out what each sector represents, you can use this fundamental formula:

$\text{Number represented} = \frac{\text{angle of sector}}{360} \times \text{total}$

Let's break this down step by step:

Take the angle of the sector you're interested in
Divide it by 360 (the total degrees in a circle)
Multiply by the total number of items in the survey

This formula works because you're finding what fraction of the whole circle your sector represents, then applying that fraction to the total count.

Worked example walkthrough

Let's work through a complete example about employment locations:

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Worked Example: Employment Location Survey

The situation: A survey asked 135 people where they worked. The pie chart shows Bath with an angle of 128°.

Step 1: Find how many people worked in Bath

Use the formula: $\text{Number} = \frac{128}{360} \times 135$
Calculate: $128 \div 360 = 0.356$ (approximately)
Then: $0.356 \times 135 = 48$ people

Step 2: Find the angle for a known quantity If we know 15 people worked in the "Other" category:

Rearrange the formula: $\text{Angle} = \frac{\text{number}}{\text{total}} \times 360$
Calculate: $\frac{15}{135} \times 360 = 40°$

Step 3: Find a quantity when you know the angle If Swindon's angle is 32°:

$\text{Number} = \frac{32}{360} \times 135 = 12$ people

Working backwards from angles

Sometimes you'll need to find an angle when you don't know it directly. Remember that all angles must sum to 360°, so:

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Unknown angle = 360° - (sum of all known angles)

For example, if you know angles of 128°, 64°, 96°, and 40°, then: Swindon angle = 360° - 128° - 64° - 96° - 40° = 32°

Exam tips and common pitfalls

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Measuring angles: In exams, you might need to measure angles on pie charts using a protractor. Always measure from the centre of the circle to get accurate readings.

Check your work: The angles should always add up to 360°. If they don't, recheck your measurements or calculations.

Units matter: Make sure you're clear about what the "total" represents - is it people, items, percentages, or something else?

Rounding: Be careful with rounding in multi-step calculations. It's often better to keep more decimal places in intermediate steps and round only your final answer.

Common question types

You'll typically encounter three main types of questions:

Given an angle, find the quantity (using the main formula)
Given a quantity, find the angle (rearranging the formula)
Finding missing angles or quantities (using the fact that totals must equal 360°)

Remember!

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Key Points to Remember:

Pie charts display qualitative data where angles are proportional to the values they represent
All angles in a pie chart must total exactly 360°
Use the formula: $\text{Number represented} = \frac{\text{angle of sector}}{360} \times \text{total}$
You can rearrange this formula to find angles when you know quantities
Always check your work by ensuring angles sum to 360°
In exams, you may need to measure angles with a protractor, so measure carefully from the centre

Interpreting pie charts (Edexcel GCSE Statistics): Revision Notes