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# Sorting Data With Venn Diagrams

One of my favorite areas to teach in chance and data is how to use Venn diagrams to sort data. If you’re not familiar with Venn diagrams, they are used to represent data that can have overlapping categories.

# Introducing Venn diagrams

One of the ways that I introduce Venn diagrams to my students is to create two large circles with rope, hoops or tape. I first start with two separate circles and ask students to decide which category they belong to and then to place themselves into the Venn diagram. The categories can be for what you like. I might say, stand in one circle if you play tennis and stand in the other circle if you play football. Then I ask: how can we show that some people play both? Then you move the circles so that they overlap. You can then get students to rearrange themselves to then stand in the overlapping part if they play both. You can also ask your students: where do you stand if you play neither sports? Again your students arrange themselves to stand on the outside of both circles if they play neither sport.

There are many ways that you can extend and adapt the above idea even further. Here are just a few that my students have enjoyed participating in.

1. Include a third group such as netball. Again, start with the circle separate and ask: how could we show that some people play both netball and tennis? How could we show that some people play the 3 different sports? Then move the circle so that it overlaps with the first 2 and then get students to rearrange themselves to be standing in the appropriate place.
2. Try sorting students with other categories as well. You could sort according to those students who like pizza and those who don’t like pizza. You could also include categories for pet ownership or other types of food, such as fruit.
3. Have your students conduct surveys with students in the class. They could collect data on the two sports students watch on TV regularly, such as cricket or football. Or which of the following do you use regularly to communicate with friends – telephone or email. Then have your students represent the results in a Venn diagram.
4. You could also give your students data in a table and then get them to use that data to represent it in a Venn Diagram, as in the picture below.
5. Encourage your students to make statements about the various Venn diagrams. For example, Tom likes pizza and pies and Amy likes pies, but not pizza or chips.
6. You could also turn using Venn diagrams into a barrier game. Have a Venn diagram template with as many circles that suit the level of your students. Label each circle with any categories that your students have been looking at. Have your students work with a partner. One student places the letters of the alphabet from A-M in various positions in the diagram. Then that student describes the placement of each letter to the other student who then places that letter in the position described on a blank Venn diagram. At the end the students compare copies.