Module 2 (M2) - Handling data - Venn diagrams

Part ofMathsM2: Handling data

Venn diagrams

A Venn diagram shows the relationship, in a visual way, between groups of different things.
They are used in many areas of life to classify items as well as highlighting similarities and differences.

Venn diagrams with 2 circles are shown in Module 1 (M1) Venn diagrams

Venn diagrams can have three circles:

A Venn diagram with 3 intersecting circles.

Example

Venn diagram showing the pizza toppings chosen by a group of friends.

  1. How many chose cheese?

  2. How many chose pepperoni and cheese?

  3. How many chose cheese but not mushroom?

1. How many chose cheese?

18 + 6 + 5 + 3 = 32

32 choose cheese.

2. How many chose pepperoni and cheese?

6 + 5 = 11

11 choose pepperoni and cheese.

3. How many chose cheese but not mushroom?

18 + 6 = 24

24 choose cheese but not mushroom.

Question

There are 150 pupils in Year 11 sitting some, if not all, of the following examinations: English, Maths and Science.

  • 15 pupils are sitting both English and Maths but not Science
  • 20 pupils are sitting Science and Maths but not English
  • 18 pupils are sitting Science and English but not Maths
  • 8 pupils are sitting all three exams
  • 65 are sitting Science in total
  • 55 are sitting English in total
  • 72 are sitting Maths in total

How many pupils do not sit any of these examinations?

Draw a Venn diagram to help you answer this question.

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