Frequency Trees
A frequency tree is a diagram that splits a total group of people or items into branches, showing how the frequencies divide into smaller categories at each stage, such as splitting a survey group by whether they walk or cycle. Missing branch values are found using addition and subtraction, since each set of branches from a node must add up to that node's own value.
Before you start
Make sure you're comfortable with these topics first:
Method
- Start from the known total and work out any missing branch value on the first split by subtracting the known branch from the total.
- Move along to the second-level branches, using the same rule: the branches from a node must add up to the value at that node.
- Fill in each missing value one at a time, checking that every set of branches sums correctly at each level.
- Use the completed tree to answer probability questions by writing the relevant frequency over the total frequency.
- For 'of these' style questions, such as a fraction of one branch, apply the fraction or percentage to that branch's own value, not the overall total.
Worked example
A survey asked 80 people whether they prefer walking or cycling to work. 34 of them said they prefer walking. Complete the frequency tree, then find the probability that a randomly chosen person prefers cycling. Give your answer as a fraction.
- The two branches (walking and cycling) must add up to the total, 80.
- Cycling = 80 - 34 = 46.
- Probability of cycling = number who cycle / total = 46/80.
- Simplify the fraction: 46/80 = 23/40.
- Final answer: 23/40.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A survey of 70 students asked whether they own a bicycle. 41 of them said yes. (a) Complete the frequency tree by working out the number of students who do not own a bicycle. (2) (b) One of the 70 students is chosen at random. Write down the probability that this student does not own a bicycle. Give your answer as a fraction. (1)
A gym has 90 members. 3/5 of the members attend classes in the evening. (a) Work out the number of members who attend classes in the evening. (2) (b) Of the members who attend evening classes, 1/9 also use the swimming pool. Work out the number of evening-class members who use the pool. (2)
A survey of 150 customers recorded whether they bought a hot or cold drink, and whether they also bought a cake. The completed frequency tree shows: Total = 150; Hot drink = 90 (of which Cake = 36, No cake = 54); Cold drink = 60 (of which Cake = 21, No cake = 39). (a) Write down the number of customers who bought a cold drink and a cake. (1) (b) One customer is chosen at random from the 150. Work out the probability that this customer bought a hot drink and did not buy a cake. Give your answer as a fraction in its simplest form. (2) (c) Work out the total number of customers who bought a cake. (2)
See real past-paper questions on frequency trees, organised by topic with official mark schemes →
Free printable worksheet
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