Pie Charts
What is a pie chart?
- A pie chart is a circle which is divided into slices (sectors) to show proportion
- They show the relative size of categories of data compared to each other, rather than their actual size or number
- For example if we were looking at the proportions of men and women working in a company, we are more interested in the relative sizes than the actual numbers of men and women
- There are 360° in a circle, and we can use this to help us calculate the size of each slice of the pie chart
How do I draw a pie chart?
- This is shown easiest through an example
- The following data is collected for a class of 30 students about their favourite colour
Colour |
Red |
Purple |
Blue |
Green |
Yellow |
Orange |
Students |
11 |
4 |
9 |
3 |
2 |
1 |
- STEP 1 – Find the number of degrees that represents 1 student
There are 30 students in total, so 360° = 30 students
Divide both sides by 30, so 12° = 1 student - STEP 2 - Calculate the angle for each category by finding a fraction of 360°
11 students out of 30 said red was their favourite colour, so this is
4 students out of 30 said purple, so this is
Repeat this for each category, they should sum to 360° in total
Colour |
Red |
Purple |
Blue |
Green |
Yellow |
Orange |
Students |
11 |
4 |
9 |
3 |
2 |
1 |
Angle |
132° |
48° |
108° |
36° |
24° |
12° |
- STEP 3 – Draw the pie chart, using a protractor to measure the angles
Start by drawing a vertical line from the centre of the circle to the top ("12 o'clock")
Then use your protractor to measure the first angle, and draw a line to this point
Move your protractor to this line, and repeat for each category
You should include a key or labels to show which slice represents which category
How do I interpret a pie chart or find missing information?
- It is easy to spot from a pie chart which category is the largest or smallest proportion, but you may be asked to do something more advanced like finding some missing information
- Remember that all of the data is represented by 360°
- You can use this to find either how many degrees each person/piece of data is represented by, or how many people/pieces of data 1 degree represents
- For example if you are told that there is a slice measuring 30° which represents 15 people
- 30° = 15 people
- 1° = 0.5 people (by dividing by 30)
- 2° = 1 person (by dividing first statement by 15 or doubling the second statement)
You can then use this information to help solve problems or find missing information
Examiner Tip
- If you are given a pie chart in an exam, it may not be to scale
- If it is not to scale, do not try to use your protractor to measure it!
- You will instead have to use the above methods to calculate the information you need
Worked example
The following pie chart is created to show the total value of items stocked in a sports shop for 4 different sports.
Using the angle marked on the pie chart, and the fact that the shop stocks $12 000 worth of Golf items, find the total value of the shop’s stock across the 4 sports.
The angle marked on the diagram is 90°.
So a quarter of the stock is for Golf.
We can multiply this by 4 to find the total value of the shop’s stock.
Total value is $48 000
Given that the angle on the pie chart for Tennis is 72°, find the value of Tennis items the shop stocks.
The fraction of the value of the shop’s stock will be the same as the fraction of the circle for each category.
Therefore the value of tennis items will be
Value of tennis items is $9 600