We can arrange information in charts, diagrams and graphs to make information more quickly. Venn diagrams are circular diagrams organizing the information. View the example below.

Police Alternate Response Unit Members: Sean, Karen, Jeff, Trevor, Kelly and Deland

Police Primary Response Unit Members: Mike, Joanne, Susan, Trevor, Dean, Ron, Nicole and Deland

You can see that Deland, Trevor and Nicole are members of both units. The diagram can be redrawn as follows:

If another group were added Community Response Unit including Deland, Bill, Geoff and Carol, the diagram would be adapted to look like below.

An example of solving problems with Venn diagrams is outlined below.

Example:

Sports teams at the local high school were divided in the following manner:

Basketball: 42
Baseball: 36
Hockey: 47

Basketball and Baseball: 14
Basketball and Hockey: 12
Baseball and Hockey: 8

Basketball, Baseball and Hockey: 3

How many students were participating in sports teams?

Answer:

Begin by drawing three circles representing the three intersecting sports.

The first step is to place the 3 in the middle representing people involved in all three sports.

The area just above the three where the intersection of baseball and basketball players is represented you place the number of players involved in both sports (14) but first subtract (3) to account for players already represented playing all three sports. The total is 11. You do this with the other segments where students play two sports (9 and 5).

Finally the players only playing one sport are separated by taking the total number of players in a sport (47 in hockey) and subtracting the hockey players already accounted for (3 playing all three sports, 5 playing hockey and baseball, and 9 playing basketball and hockey). The result is 30.

If you add up all of the players now segmented, you will have the total number of different students playing sports.

19 + 11 + 17 + 9 + 3 + 5 + 30 = 94