Angles for pie charts Revision Notes for AQA GCSE Statistics

Angles for pie charts

Pie charts are brilliant visual tools for showing how data is divided into different categories. The key to creating accurate pie charts lies in understanding how to calculate the correct angles for each sector. Each sector's size must be proportional to the data it represents, and since a complete circle contains 360°, we need to work out what fraction of this total each category should take up.

The angle formula

When creating pie charts, you'll need to convert your data into angles that add up to exactly 360°. The essential formula you need to master is:

$\text{Angle} = \frac{\text{number to be represented}}{\text{total}} \times 360°$

This formula works by finding what proportion each category represents of the total, then multiplying by 360° to find the corresponding angle in the pie chart.

Step-by-step method

Here's the systematic approach you should follow every time:

Calculate the total first - Add up all the numbers in your data set
Apply the formula - Use the angle formula for each category
Check your work - All angles must add up to exactly 360°
Draw accurately - Use proper equipment to construct your pie chart

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Worked Example: Blood types

Let's work through a complete example using blood type data:

Table

Data given:

Type O: 30 people
Type A: 24 people
Type B: 12 people
Type AB: 6 people

Step 1: Find the total Total = 30 + 24 + 12 + 6 = 72 people

Step 2: Calculate each angle

For Type O: $(30 ÷ 72) × 360° = 150°$

For Type A: $(24 ÷ 72) × 360° = 120°$

For Type B: $(12 ÷ 72) × 360° = 60°$

For Type AB: $(6 ÷ 72) × 360° = 30°$

Step 3: Check the total $150° + 120° + 60° + 30° = 360°$ ✓

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Worked Example: Types of flats

Here's another example to reinforce the method:

Data given:

Bedsits: 90 flats
1-bedroom: 42 flats
2-bedroom: 30 flats
3-bedroom: 18 flats

Step 1: Find the total Total = 90 + 42 + 30 + 18 = 180 flats

Step 2: Calculate the angle for bedsits Angle for bedsits = $(90 ÷ 180) × 360° = 180°$

Notice that bedsits represent exactly half the total (90 out of 180), so they take up half the circle (180° out of 360°).

The remaining angles would be calculated using the same method for the other categories.

Essential equipment and tips

To draw accurate pie charts, you'll need:

Compass for drawing the circle
Protractor for measuring angles accurately
Ruler for drawing straight lines to create sectors

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Important exam tips:

Always work out the total before calculating individual angles
Double-check that all your angles add up to 360° - if they don't, you've made an error
Remember to label each sector clearly
Show all your working clearly in exams
Round carefully - sometimes small rounding errors can cause totals that don't quite reach 360°

Common exam trap: Students often forget to find the total first, or they add up their angles incorrectly. Always take time to check your arithmetic.

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Key Points to Remember:

The pie chart angle formula is: $\text{Angle} = \frac{\text{number to be represented}}{\text{total}} \times 360°$
Always calculate the total of all your data first
All angles in a pie chart must add up to exactly 360°
Use proper equipment (compass, protractor, ruler) for accurate construction
Check your working by adding up all calculated angles - they should equal 360°

Angles for pie charts (AQA GCSE Statistics): Revision Notes