Pie charts (Edexcel GCSE Maths): Revision Notes
Pie charts
What are pie charts?
A pie chart is a circular diagram used to display data visually. It shows different categories as sectors (slices) of a circle, where each sector's size represents the proportion of that category in the total dataset.
In your GCSE exam, you might need to interpret information from a pie chart or create one from a frequency table. Pie charts are particularly useful for showing how different parts make up a whole dataset.
Understanding angles in pie charts
The key principle behind pie charts is that there are 360° in a complete circle. This means that all the sectors in your pie chart must add up to exactly 360°.
Each item or person in your dataset is represented by an equal share of these 360°. To find out how many degrees each item should get, you divide 360° by the total number of items in your dataset.
Formula:
Calculating sector angles
Once you know the angle per item, you can calculate the angle for each category by multiplying:
Sector angle = number of items in category × angle per item
For example, if you have 120 students total and each student represents 3°, then:
- A category with 22 students would have an angle of
- A category with 20 students would have an angle of
Always check your work by adding all the sector angles together - they should equal 360°.
How to draw a pie chart
Follow these steps to create an accurate pie chart:
- Add an 'Angle' column to your frequency table and calculate each sector angle
- Find the total frequency and divide 360° by this number to get the angle per item
- Multiply the angle per item by each category's frequency to find each sector angle
- Check that all your sector angles add up to 360°
- Draw a circle using compasses with a radius of at least 3cm
- Draw a vertical line from the centre to the edge of the circle as your starting reference
- Use a protractor to measure and draw each angle carefully in order from your reference line
- Label each sector clearly with the category name
Drawing Tip: Use a radius of at least 3cm to ensure your pie chart is large enough to measure angles accurately with your protractor.
Worked example
Worked Example: Creating a Pie Chart for Farm Trees
A farm has 40 fruit trees shown in this frequency table:
| Type of fruit tree | Number of trees |
|---|---|
| Apple | 12 |
| Plum | 5 |
| Pear | 14 |
| Peach | 9 |
Step 1: Calculate angle per tree =
Step 2: Calculate each sector angle:
- Apple:
- Plum:
- Pear:
- Peach:
Step 3: Check: ✓
Step 4: Draw your circle and use a protractor to measure each angle from your reference line, working around the circle in order.
Interpreting pie charts
When reading a pie chart, look for:
- Which sector is the largest (most popular category)
- Which sector is the smallest (least popular category)
- How the sectors compare to each other in size
- What fraction or percentage each sector represents
Reading Strategy: Start by identifying the largest and smallest sectors, then work out approximate fractions. A quarter of the circle is 90°, half is 180°, and three-quarters is 270°.
Practice opportunity
Try creating a pie chart for this school canteen data showing lunch choices made by 90 students:
| Lunch choice | Number of students |
|---|---|
| Salad | 21 |
| Stew | 9 |
| Pizza | 45 |
| Curry | 15 |
Practice Hint: Remember to start by drawing a circle with a radius of at least 3cm, then calculate your angles before using your protractor. Each student will represent .
Key Points to Remember:
- Pie charts show parts of a whole using circular sectors
- All sector angles must add up to 360° - always check this
- Calculate angle per item by dividing 360° by the total frequency
- Use compasses and a protractor for accurate construction
- Label each sector clearly with the category name