Pie charts (AQA GCSE Maths): Revision Notes
Pie charts
What is a pie chart?
A pie chart is a circular graph that shows data as sectors (slices) of a circle. Each sector represents a category or group from your data. The size of each sector is proportional to the frequency or value it represents.
Pie charts are particularly useful for showing:
- Parts of a whole
- Percentages or proportions
- Comparing different categories within a dataset
Pie charts work best when you have between 3-7 categories. Too many categories can make the chart difficult to read and interpret.
Key facts about pie charts
Understanding the mathematical foundation of pie charts is essential for creating and interpreting them accurately.
A complete circle contains 360 degrees (360°)
This means that all the sectors in your pie chart must add up to exactly . This is how you can check your work is correct.
When you have data to represent, you need to work out what angle each item should have:
- Angle per item =
How to interpret pie charts
When reading a pie chart, look for:
- Which sector is the largest (represents the most popular category)
- Which sector is the smallest (represents the least popular category)
- How the sectors compare to each other in size
- What fraction or percentage each sector represents
For example, if half the students chose football as their favourite sport, the football sector would take up half the circle (180°).
A quick way to estimate proportions is to remember that:
- Quarter of the circle =
- Half of the circle =
- Three quarters of the circle =
How to create pie charts from frequency tables
Creating accurate pie charts requires the right tools and a systematic approach to ensure precision in your construction.
Tools you need:
- Sharp pencil
- Compass (to draw the circle)
- Protractor (to measure angles)
- Ruler (to draw straight lines)
Step-by-step method:
Step 1: Add an 'Angle' column to your frequency table
Step 2: Calculate the angle for one item
- Divide by the total frequency
- Formula:
Step 3: Calculate the angle for each category
- Multiply the frequency of each category by the angle per item
- Formula:
Step 4: Check your angles add up to 360°
- Add all your calculated angles together
- If they don't equal , check your calculations
Step 5: Draw your pie chart
- Use compasses to draw a circle (at least 3cm radius works well)
- Draw a vertical line from the centre to the edge
- Use your protractor to measure each angle from this line
- Draw each sector carefully in order
- Label each sector clearly
Always start measuring your angles from a vertical line at the top of the circle. This is the standard convention and makes your chart easier to read.
Worked example
Worked Example: Creating a Pie Chart for Farm Trees
A farm has 40 fruit trees. Here's the data:
| Type of fruit tree | Number of trees | Angle |
|---|---|---|
| Apple | 12 | |
| Plum | 5 | |
| Pear | 14 | |
| Peach | 9 |
Step-by-step calculations:
- Total trees =
- Angle for 1 tree =
- Calculate each sector angle using the formula above
- Check: ✓
Interpretation: The largest sector represents pears (), and the smallest represents plums ().
Exam tips
Successful pie chart questions require both mathematical accuracy and good construction technique.
Essential exam strategies:
- Always show your working when calculating angles
- Remember to check that your angles add up to 360°
- Draw your circle large enough to label sectors clearly
- Start measuring angles from a vertical line at the top
- Use a sharp pencil for accurate construction
- In exam questions, you may need to interpret existing pie charts or construct new ones from given data
Key Points to Remember:
- A complete circle has 360 degrees
- Calculate the angle per item by dividing by the total frequency
- Each sector angle = frequency × angle per item
- Always check your angles add up to
- You need a compass, protractor, and sharp pencil to construct pie charts accurately
- Pie charts are best for showing parts of a whole with 3-7 categories