Module 1 (M1) - 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 diagram of a bird and a kangaroo in one circle, a fish and a crab in the other. A penguin is in the intersection and a giraffe outside both circles. The first circle shows two legged animals. The second circle shows water animals. A giraffe has 4 legs and is not a water animal. It does not fit into either. here they overlap, the intersection, shows the penguin which is both two legged and a water animal.

Solving problems with Venn Diagrams

Example

A class of children were asked if they play football or swim.

18 said they play football, 13 swim and 6 play football and swim.
Two children do not play football or swim.

How many children are in the class?
How many children do not play football?

Drawing a Venn diagram makes answering this type of question easier.

Start by drawing a rectangle containing two intersecting circles as there are two sports.

Label one football and the other swimming.

Venn digram of two circles labelled football and swimming. There are 6 children who do both sports so put a 6 in the intersection. Two children do not play football or swim so put a 2 inside the rectangle but outside the circles.

Venn diagram of Football v Swimming. 18 children play football, this includes the 6 who do both. Therefore, the number of children who play football and do not swim is 18 – 6 = 12. 13 children swim, this includes the 6 who do both. Therefore, the number who swim and do not play football is 13 – 6 = 7

Using the Venn diagram to answer the questions

To find the total number of children add all the numbers inside the rectangle together.

The total number of children in the class is 12 + 6 + 7 + 2 = 27

To find the number of children who do not play football cover up the circle with football and add the other numbers.

The number of children who do not play football is 2 + 7 = 9

Venn diagram showing the subjects studied by pupils in a year group.

How many pupils study Chemistry?
How many pupils study History but not Chemistry?
How many pupils are in the year group?

Question

In a survey, 200 customers were asked their views on being an ethical consumer.

89 customers said they like to buy Fairtrade products when they can.
131 customers preferred to buy local products.
45 customers were keen to buy products from both the Fairtrade and the local range.
The remaining customers had not considered either Fairtrade or locally produced products.

How many customers had not considered either?

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