Pie Charts (Edexcel GCSE Maths: Foundation)

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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
Colour Red Purple Blue Green Yellow Orange
Students 11 4 9 3 2 1

  

  • Write the frequencies as fractions of the total number of students, 30
Colour Red Purple Blue Green Yellow Orange
Students 11 4 9 3 2 1
Fractions 11 over 30 4 over 30 9 over 30 3 over 30 2 over 30 1 over 30

   

  • Find the angles of the sectors by multiplying each fraction by 360° 
    • Then check all angles add up to 360°
Colour Red Purple Blue Green Yellow Orange
Students 11 4 9 3 2 1
Fractions 11 over 30 4 over 30 9 over 30 3 over 30 2 over 30 1 over 30
Angles 132° 48° 108° 36° 24° 12°

 

  • 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)

A protractor measuring the first angle in a pie chartA protractor measuring the second angle in a pie chart

A pie chart showing the favourite colours of students

 

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)

Examiner Tip

  • 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.
 

[not to scale]   

A pie chart showing the value of items in a sports shop

 

(a)

Given that the shop stocks $12 000 of golf items, find the total value of the shop’s stock. 

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° = 3 ×12 000

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.

It is quickest to find the fraction 72 over 360 of the total value, found in part (a)

72 over 360 cross times 48 space 000 equals 9 space 600

The value of tennis items is $9 600

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Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.