Bigger bar charts and rounding · Usually met around P4
Venn and Carroll diagrams
Count the overlap only once.
How to do it
Method
Count the overlap only once
13 + 11 − 5 = 19
Another way
Add each part
8 + 5 + 6 = 19
In full
A Venn diagram sorts with two rings: A on the left, B on the right. Where they overlap is what fits both; outside both rings is what fits neither. Everyone who likes A = only A + the overlap; at least one = only A + overlap + only B. When you only know the totals for A and B, A + B counts the overlap twice, so take it away once: 13 + 11 − 5 = 19. A Carroll diagram works the same way: add the cells row by row or column by column and the total stays the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like swimming altogether?
Show the answer and working
Answer: 16 children
Everyone in ring A likes swimming: 11 in A only plus 5 in the overlap, 16.
Example 2
The Venn diagram shows how many children in a group like swimming (A) and running (B). How many children are in the group?
Show the answer and working
Answer: 32 children
Add all four parts: 8 + 8 + 14 + 2 = 32 (those outside the rings too).
Example 3
The Venn diagram shows how many children in a group like swimming (A) and running (B). More children like swimming than running.
True or false?
Show the answer and working
Answer: False
Swimming: 2 + 11 = 13; running: 11 + 9 = 20. Compare them.
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