Tables & Venn Diagrams
Extracting data from tables and two-way tables, and using Venn diagrams to solve problems.
What is Tables & Venn Diagrams?
Tables and Venn diagrams are two common ways of organising and displaying data in the 11+ exam. You need to be able to read values, fill in missing values, and use the data to answer questions.
Two-way tables show data sorted by two categories (e.g. boys/girls and sport preferences). Venn diagrams use overlapping circles to show items that belong to one group, both groups, or neither.
Step-by-Step Method
For tables, use row and column totals
If a value is missing, use the total to work backwards: missing value = total – known values.
For Venn diagrams, start with the overlap
Always fill in the intersection (middle section) first, then work outwards.
Find the “outside” region
The region outside all circles represents items in neither group. Total – (all circle values) = outside.
Do not double-count the overlap
Items in the overlap belong to BOTH groups, not just one. Be careful when adding up totals.
Check all regions add up to the total
All the numbers in a Venn diagram (including outside) should add up to the grand total.
Worked Examples
A table shows: Boys who like football = 12, Boys who like tennis = 8, Total boys = 20. Girls who like football = 9, Total who like football = 21. Find girls who like tennis if total students = 35.
Working
- Girls total = 35 – 20 = 15.
- Girls who like tennis = 15 – 9 = 6.
- Check: tennis total = 8 + 6 = 14. Football total = 12 + 9 = 21. All totals: 21 + 14 = 35. Correct!
30 children: 18 like chocolate, 12 like vanilla, 7 like both. How many like neither?
Working
- Only chocolate: 18 – 7 = 11.
- Only vanilla: 12 – 7 = 5.
- Both: 7.
- Total in circles: 11 + 5 + 7 = 23.
- Neither: 30 – 23 = 7.
From a frequency table: red = 5, blue = 8, green = 3, yellow = 4. What fraction chose blue?
Working
- Total = 5 + 8 + 3 + 4 = 20.
- Fraction choosing blue = 8/20 = 2/5.
Common Mistakes
Double-counting the overlap in Venn diagrams (adding 18 + 12 = 30 instead of 18 + 12 – 7 = 23).
Remember: the overlap is already included in both circle totals. Subtract it once.
Forgetting the “neither” region outside the circles.
Always consider that some items might not belong to any group.
Misreading two-way table rows and columns.
Read the row header and column header carefully to identify exactly what each cell represents.
Top Tips
- In Venn diagrams, always start from the middle (overlap) and work outwards.
- Check: all regions of the Venn diagram must add up to the total.
- In two-way tables, each row total and each column total must add up to the grand total.
- Draw a Venn diagram even when the question does not ask for one – it helps organise your thinking.
Ready to practise?
Put these techniques into action with our free practice papers.
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