Skip main navigation

New offer! Get 30% off one whole year of Unlimited learning. Subscribe for just £249.99 £174.99. New subscribers only. T&Cs apply

Find out more

Using Venn Diagrams

In this article, we consider the use of Venn Diagrams to represent experimental results and expected frequencies.
A Venn diagram showing the expected frequencies for 'The dog ate my homework!'
We use a variety of representations for both experimental and expected frequencies.

We believe that there is no single best way to represent data – different styles of presentation highlight different aspects of the data, and are more or less useful in different circumstances. So far, frequency trees have been our main form of representation, but it is worth considering the features of some alternative representations.

The diagram above shows the ‘Dog ate my homework’ expected frequencies as a Venn diagram. There is no one ‘correct’ way to set up the diagram here – there are several correct ways in which the circles could be labelled. There are also some ways of labelling the circles that do not result in useful diagrams!


  • Can you explain how this diagram works?
  • What are the advantages and disadvantages of this form of representation?
  • Could you complete a Venn Diagram for the same data with different sets labelled (e.g. ‘Truthful’ and ‘Believed’)?
  • Could you complete a Venn Diagram to show the expected frequencies for the variation introduced in the previous step (where Mr D treats all students alike, whether or not he suspects them of lying?)

This article is from the free online

Teaching Probability

Created by
FutureLearn - Learning For Life

Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now