Maths
What is a Venn diagram?
Quick answer
A Venn diagram uses overlapping circles to sort things into groups. The overlap shows what belongs to both groups, and the outside shows what belongs to neither.
In one sentence
A Venn diagram shows how groups overlap by drawing each group as a circle inside a box.
Explained
A Venn diagram sorts things into groups called sets. Each set is a circle. If something belongs to a set, it goes inside that circle. The box around the circles stands for everything you are sorting. Anything that fits neither set sits in the box, outside the circles.
The clever part is where two circles overlap. This middle part, called the intersection, holds things that belong to both sets. Everything in at least one circle is called the union.
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Example: Numbers 1 to 12, sorted into "multiples of 2" and "multiples of 3".
- Only multiples of 2: 2, 4, 8, 10
- Only multiples of 3: 3, 9
- In both (the overlap): 6 and 12
- In neither: 1, 5, 7, 11
Venn diagrams also help with counting. Suppose 30 pupils are asked about hobbies. 18 play football, 12 play chess and 5 do both. In the overlap write 5. Football only is 18 − 5 = 13, and chess only is 12 − 5 = 7. So 13 + 5 + 7 = 25 play at least one, and the other 30 − 25 = 5 play neither. Always fill in the overlap first, to avoid counting anything twice.
You can use them to sort factors and multiples, shapes, animals or words. The diagram is named after the English logician John Venn. They are also used in probability, to show events that can happen at the same time.
Examples
| Circles | Overlap |
|---|---|
| Even numbers and multiples of 5 | 10, 20, 30 … |
| Animals with wings and animals that lay eggs | birds |
| Square shapes and shapes with right angles | squares |
Common mistakes
- Double counting. If 5 children are in both groups, do not count them in each circle's total as well as the overlap.
- Forgetting the outside. Items in neither group still belong in the box.
- Putting an item in the wrong part. Check each item against both descriptions.
Quick quiz
Venn diagrams
Check what you know with 4 quick questions.
Question 1 of 4
What does the overlap of two circles show?
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Related topics
Probability
Probability measures how likely something is to happen, on a scale from 0 (impossible) to 1 (certain). A fair coin landing heads has a probability of 1/2.
Bar charts
A bar chart shows data using bars of different lengths. The longer the bar, the bigger the number. In the US it is usually called a bar graph.
Factors and multiples
Factors are numbers that divide exactly into a number (the factors of 12 are 1, 2, 3, 4, 6 and 12). Multiples are the numbers in its times table (12, 24, 36…).
Line graphs
A line graph shows how something changes over time. Points are plotted on a grid and joined by a line, so you can see rises, falls and patterns at a glance.
Pie charts
A pie chart is a circle divided into slices that show parts of a whole. A bigger slice means a bigger share, and all the slices together make 100 percent, or 360 degrees.
Tally charts
A tally chart is a table that counts things with little marks. Each mark is one, and every fifth mark crosses the four before it, so you can count in fives.