Numeracy Skills

3.6. Venn and Carroll Diagrams

Finally we come to Venn and Carroll diagrams, both of which offer an effective, if not dissimilar method for categorising information.

Suppose we were to say of the cats of Baal that they fall in to the category of being either tabby, or non-tabby, then we have a set of four possibilities into which each of the entire cat-population must fall. These are:

1. Non-tabby, can’t talk
2. Non-tabby, can talk
3. Tabby, can’t talk
4. Tabby, can talk

Each of these combinations can be presented in a Venn or Carroll diagram, where the overall population (universal set) is represented by the rectangle/square, and the different subsets (being tabby, non-tabby, talking or not talking), by the spaces enclosed within this area.

Note how Venn diagrams are helpful in being able to depict where these qualities can overlap, whilst in the Carroll diagram, each numbered space corresponds to the type of variable we are dealing with (this can be made clearer by inserting the amount/type etc. of entity adjacent to each number).

More complex data can be accommodated for by more complex diagrams.

Note, however, that beyond a range of eight variables, such diagrams become too complicated for practical purposes.

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Interesting sub-notes:

Carroll diagrams are also known as Lewis Carroll's squares, since the author of the Alice in Wonderland novels was also a gifted mathematician and the inventor of these diagrams.

For his 180th birthday on August 4th 2014, Google made a 'Doodle' to celebrate John Venn and his diagrams.