A Venn diagram showing the expected frequencies for 'The dog ate my homework!'
Expected frequencies can also be shown on a Venn Diagram

Using Venn Diagrams

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?)

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This article is from the free online course:

Teaching Probability

Cambridge University Press