Topics / Maths
Venn and Carroll diagrams
These diagrams sort things by two properties at once. A Venn diagram uses overlapping circles; a Carroll diagram uses a grid with 'is' and 'is not' for each property. Questions ask where items go or how many are in each part.
What is tested
- Placing numbers or items in the right region
- Using the overlap (both properties) and the outside (neither)
- Working out a missing number from totals
Worked example
In a class of 30, 18 like football, 15 like tennis and 5 like neither. How many like both?
- Children who like at least one sport: 30 − 5 = 25.
- Adding the two groups counts the 'both' children twice: 18 + 15 = 33.
- The extra is the overlap: 33 − 25 = 8.
Answer: 8
Exam-day checklist
- Fill in the overlap first when you can.
- Remember the space outside the circles (neither).
- Each item goes in exactly one region.
- Check the regions add up to the total.
Common mistakes
- Counting the overlap twice.
- Forgetting the 'neither' group.
- Putting an item in a circle when it only fits one property.
Try it yourself
1. Which numbers from 1 to 12 go in the Carroll diagram box for 'even' AND 'multiple of 3'?
Show answer
6 and 12
They are the only numbers up to 12 that are both even and multiples of 3.
2. A Venn diagram has circles for 'multiples of 2' and 'multiples of 5'. Which numbers from 1 to 30 go in the overlap?
Show answer
10, 20 and 30
They are multiples of both 2 and 5, i.e. multiples of 10.
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