Pie Charts (Cambridge International IGCSE Maths)

Pie charts

What is a pie chart?

• A pie chart is a circle divided into sectors which is used to present data

• The sectors represent different categories

  • They show the relative proportions of the categories
  • They do not show the actual frequencies of each category

How do I draw a pie chart?

• This is easiest explained through an example
• The following data shows the favourite colours of a class of students

• Write the frequencies as fractions of the total number of students, 30

• Find the angles of the sectors by multiplying each fraction by 360°

  • Then check all angles add up to 360°

• Draw a vertical line from the circle's centre to the top, then use a protractor to mark off the first angle

  • Draw a line from the centre to this first mark

    • Then, from this line, mark off the next angle (and so on)

Example of a pie chart

How do I solve problems with pie charts?

• Use the following facts

  • angles are proportional to the frequencies of each category
  • 360° represents the total frequency

• For harder problems, it helps to work out

  • what frequency is represented by 1°
  • what angle is represented by 1 unit of frequency

• For example, if a sector of 30° represents 15 people, then

  • 1° = 0.5 people (dividing by 30)
  • 2° = 1 person (multiplying by 2)

• These relationships can then be scaled up or down accordingly

  • If 1° = 0.5 people

    • then 360° = 180 people (multiplying by 360)

Exam Hint If the pie chart says 'not to scale', then examiners want you to use ratio and proportion methods to answer the questions. Don't measure angles using a protractor!

Worked Example The following pie chart represents the values of items stocked in a sports shop.

The diagram is not to scale.

(a) Given that the shop stocks £12 000 of golf items, find the total value of the shop’s stock.

Answer:

Find a relationship between an angle and a value

90° = £12 000

The total value is represented by 360° Multiply by 4 to get from 90° to 360°

360° = 4 ×12 000

Final answer: Total value is £48 000

You can also do this question by finding 1° first

(b) If the angle on the pie chart for tennis is 72°, find the value of tennis items that are stocked by the shop.

Answer:

It is quickest to find the fraction $\frac{72}{360}$ of the total value, found in part (a)

$\frac{72}{360}\times48000=9600$

Final answer: The value of tennis items is £9 600