GCSE-readyTwo-way tables and frequency trees
When people are sorted in two ways at once, such as year group and how they travel, two-way tables and frequency trees keep the counts organised.
Two-way tables
| Walk | Bus | Car | Total | |
|---|---|---|---|---|
| Year 8 | 12 | 9 | 7 | 28 |
| Year 9 | 10 | 15 | 7 | 32 |
| Total | 22 | 24 | 14 | 60 |
Probabilities from a table
P(Year 9 and walks) = 1060 = 16.
If you are asked about one group only, divide by that group's total: the fraction of Year 8 students who take the bus is 928.
Frequency trees
80 people: 50 adults and 30 children.
Of the adults, 35 own a bike and 15 do not. Of the children, 24 own a bike and 6 do not.
The numbers at the end of the branches add up to the total: 35 + 15 + 24 + 6 = 80.
Using the table, find the probability that a randomly chosen student travels by car.
- Car total: 7 + 7 = 14
- Grand total: 60
- 1460 = 730
Answer: 730
Use the totals to fill gaps. For probability, divide the cell by the total of the group you are choosing from. Frequency tree branches must add up to the starting number.
- Frequency
- How many times something happens or a value appears in a set of data.
- Probability
- How likely something is to happen, from 0 (impossible) to 1 (certain).
2 more questions
Try each one, then tap to check.
A two-way table shows how students travel. Year 8: walk 14, bus 8, car 6. Year 9: walk 9, bus 12, car 11. How many students travel by bus?
Show the answer
Answer: 20
8 + 12 = 20.
Year 10 has 30 students: 12 walk and 9 take the bus. How many travel by car?
Show the answer
Answer: 9
30 − 12 − 9 = 9.
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Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.