Complete a frequency tree from worded information and use it to find fractions and probabilities. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A frequency tree is a two-step story in boxes: 80 people, 45 take the bus, of those 30 have a ticket, and so on. Each pair of branches adds back to the parent box. Fill the known numbers first, then the others by subtraction. At the end, the four (or more) end-boxes must add to the start total.
A probability question hanging off a frequency tree is 'number in that end box ÷ start total' for a random person, or ÷ the relevant parent if the person is already known to be in a subgroup. Keep frequencies as whole people; do not write 22.5 people unless the question has already left the real world.
Start with the total, split into the first groups, then split each branch. Complements on a branch add to the parent. A probability from a tree is a branch-end frequency over the total (or a product of fractions along the branches).
Objectives
Write the whole group at the start.
If 30 people arrive and 18 say yes, 12 say no.
The yes group can split again, for example by age.
Key points
Fill in a frequency tree using totals, fractions and percentages from the text.
Use the rule that the two branches from any node add up to that node.
Read a probability from the tree as a fraction of the right total.
Handle 'given that' style questions by using the smaller group as the denominator.
Worked examples
Example 1
13 people were asked. 8 said yes. How many said no?
2 marks
The yes and no branches add to 13.
13 − 8 = 5.
5 people said no.
Answer: 5
Common slips
Slip: The yes and no branches add to 1. Frequencies add to the number that arrived at that point, not to 1.
Slip: 13 + 8 = 21. A missing branch is found by subtracting.
Slip: 21 people said no. More people said no than were asked.
Example 2
19 people said yes. 7 of them were under 15. How many of the yes group were 15 or over?
2 marks
The yes group splits into under 15 and 15 or over, so the two branches add to 19.
19 − 7 = 12.
12 of the yes group were 15 or over.
Answer: 12
Common slips
Slip: The under 15 and 15 or over branches add to 1. Frequencies add to the number that arrived at that point, not to 1.
Slip: 19 + 7 = 26. A missing branch is found by subtracting.
Slip: 26 of the yes group were 15 or over. That is more than the whole yes group.
Example 3
24 people were asked. 18 said yes. How many said no?
2 marks
The yes and no branches add to 24.
24 − 18 = 6.
6 people said no.
Answer: 6
Common slips
Slip: The yes and no branches add to 1. Frequencies add to the number that arrived at that point, not to 1.
Slip: 24 + 18 = 42. A missing branch is found by subtracting.
Slip: 42 people said no. More people said no than were asked.
Questions and answers
GCSE Maths frequency trees questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
17 people said yes. 4 of them were under 15. How many of the yes group were 15 or over?
Show answer
Answer: 13
The yes group splits into under 15 and 15 or over, so the two branches add to 17.
17 − 4 = 13.
M1 — The yes group splits into under 15 and 15 or over, so the two branches add to 17.
A1 — Answer 13
Question 2 Easy2 marks
18 people were asked. 11 said yes. How many said no?
Show answer
Answer: 7
The yes and no branches add to 18.
18 − 11 = 7.
M1 — The yes and no branches add to 18.
A1 — Answer 7
Question 3 Medium2 marks
22 people said yes. 7 of them were under 15. How many of the yes group were 15 or over?
Show answer
Answer: 15
The yes group splits into under 15 and 15 or over, so the two branches add to 22.
22 − 7 = 15.
M1 — The yes group splits into under 15 and 15 or over, so the two branches add to 22.
A1 — Answer 15
Question 4 Medium2 marks
23 people were asked. 14 said yes. How many said no?
Show answer
Answer: 9
The yes and no branches add to 23.
23 − 14 = 9.
M1 — The yes and no branches add to 23.
A1 — Answer 9
Question 5 Hard2 marks
27 people said yes. 10 of them were under 15. How many of the yes group were 15 or over?
Show answer
Answer: 17
The yes group splits into under 15 and 15 or over, so the two branches add to 27.
27 − 10 = 17.
M1 — The yes group splits into under 15 and 15 or over, so the two branches add to 27.
A1 — Answer 17
Question 6 Hard2 marks
28 people were asked. 17 said yes. How many said no?
Show answer
Answer: 11
The yes and no branches add to 28.
28 − 17 = 11.
M1 — The yes and no branches add to 28.
A1 — Answer 11
Question 7 Exam-style2 marks
10 people said yes. 4 of them were under 15. How many of the yes group were 15 or over?
Show answer
Answer: 6
The yes group splits into under 15 and 15 or over, so the two branches add to 10.
10 − 4 = 6.
6 of the yes group were 15 or over.
M1 — The yes group splits into under 15 and 15 or over, so the two branches add to 10.
A1 — Answer 6
Common mistakes
Most lost marks on this topic are one slip.
Making the branches add to 1.
Add them to the frequency that entered the split.
Subtracting a branch from the original total when it came from a later group.
Subtract from the group that split.
Multiplying along the path.
That is a probability tree. Here you read or add the frequencies.
Spot the slip
The branches leaving one point should add to
the number that arrived at that point
1
100
Show the slip
the number that arrived at that point Frequencies add back to the group they came from.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the calculation next to each box (e.g. 80−45=35) so a slip still earns method marks.
For probabilities, write the unsimplified fraction first (12070) and then simplify — both are usually accepted, and the first protects you.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.