Home → Curriculum Hub → Maths Lessons → Collecting Data → Drawing Frequency Trees for GCSE Maths
Ready-to-teach lesson. Includes a video tutorial, printable worksheets and GCSE exam-style practice with worked solutions.
This lesson covers drawing frequency trees from a two-way table and from a written description. The later examples add a check of the branch totals and a probability from the completed tree.
Most students can already complete a two-way table frequency trees are an extension of this and later followed by probability trees.
I teach frequency trees after two-way tables. The next lesson is designing questionnaires and spotting bias. For a harder follow-up, use the two-way tables and frequency trees problem-solving pack.
Watch the handedness example first. Counts move from the two-way table onto the tree, one branch at a time. Download the handout to work along with the video, then try the worksheet below.
Key topics: two-way tables, frequency trees, written descriptions, checking branch totals, probability from a frequency tree. Download handout.
A frequency tree shows how a total splits into actual counts. A probability tree shows the chance of each branch. They look similar, but the type of number on the branch is different.
Frequencies are whole numbers. Each pair of branches adds back to the node before it. Probabilities on a split add to 1.
The same data can live in a two-way table. The tree makes the order of the split visible. That order matters when a fact says “23 of the 49 students who came by bicycle are boys”.
Questions 1 to 3 start with a given tree and a short list of facts. Students complete the frequencies, then read a count or a probability from the finished diagram.
Questions 4 to 6 drop the scaffolding. One item uses a fraction of an amount on a branch. The last question has no probability part, so the check is the tree itself.
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The starter recaps two-way tables before the tree appears. Students fill the missing cells from the given totals. The arithmetic is the same work they will later do on the branches.
Prompts / Questions to consider
The teaching example gives a completed two-way table and a blank tree. Students transfer each count onto its branch. The template is already drawn, so the task is matching, not constructing the shape.
That matching is the literacy demand. Students who can add and subtract still stall if they cannot see which phrase belongs on which branch. Keep the tree on the board and highlight one fact at a time.
Prompts / Questions to consider
The plenary drops the table. Students now build a tree with six combinations from a written description. The first split is boys and girls, not the three methods of travel.
Hide the template first if you want to see who can choose that split. The text only states that 56 of the 120 students are boys. The girls total of 64 has to be found.
Boys bicycle is 23, taken from “23 of the 49 students who came by bicycle are boys”. Girls bicycle is then 26. Boys car is 26, girls walking is 16, and the six leaves add to 120.
Prompts / Questions to consider
More able: Hide the plenary template and ask them to choose the first split from the text. Then set a probability from a restricted group, as in the gym and coffee questions.
Less able: Start the worksheet at the two-way table questions. Keep the tree template visible and highlight each phrase before the number is placed.
| Phase | Focus | Time |
|---|---|---|
| Starter | Complete the eye-colour two-way table | 8 min |
| Development | Transfer the handedness table onto a given tree | 12 min |
| Check | Add the leaf frequencies back to the previous node | 5 min |
| Main / stretch | Independent worksheet, starting at the table questions if needed | 15 min |
| Plenary | Six-outcome travel tree from a written description | 10 min |
Use this checklist after the lesson or as a revision self-check.
Try these GCSE-style questions on drawing frequency trees, then reveal the solutions to check your working. Select the image to view it full screen.
Complete the frequency tree for 180 apartments, then find the probability of no balcony and no garden, or both a balcony and a garden.
The root is 180. No balcony is 70, so balcony is 110. No balcony and no garden is 45, so no balcony and garden is 25.
Garden in total is 105, so balcony and garden is 80. Balcony and no garden is then 30. Check: 45 + 25 + 30 + 80 = 180.
The two events in part b are 45 and 80. Probability = 125/180 = 25/36.
Complete the workers’ coffee survey tree, then find the probability that a person chosen from those who like coffee is a woman.
The printed slide is missing a fourth fact. The video handout adds: 10 of the men do not like coffee. The tree cannot be completed uniquely without it.
Women 42, so men 28. Like coffee 49, so do not like coffee 21. Men who do not like coffee 10, so men who like coffee 18.
Women who do not like coffee 11, so women who like coffee 31. Check: 18 + 31 = 49. Probability = 31/49.
Complete the frequency tree for 75 rabbits, then find the probability that a rabbit chosen at random is an adult Dutch rabbit.
Adults 48, so kittens (children on the tree) 27. Adult lop-eared 20, so adult Dutch 28.
Kitten Dutch 15, so kitten lop-eared 12. Check: 20 + 28 + 12 + 15 = 75.
Probability of an adult Dutch rabbit = 28/75.
Use the completed frequency tree of 36 flowers to fill the two-way table of white and red roses and tulips.
Each leaf of the tree is a cell of the table. Rose white 10, rose red 12, tulip white 6, tulip red 8.
Row checks: 10 + 12 = 22 and 6 + 8 = 14. Column checks: 10 + 6 = 16 white and 12 + 8 = 20 red.
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A frequency tree is a branching diagram that shows how a total splits into actual counts. Each pair of branches adds back to the node before it. The same data can also be written in a two-way table.
A frequency tree shows frequencies, which are whole numbers. A probability tree shows probabilities, which add to 1 along a split. Students often copy the tree shape and put the wrong type of number on the branches.
Put the grand total at the root. The row totals, or the column totals, become the first pair of branches. Each cell of the table becomes a leaf.
Add the numbers at the end of each pair of branches. They must equal the number at the previous node. If a pair does not recover its parent, that split is wrong.
Write the frequency of the event over the correct total. For a group that has already been chosen, use that group’s total, not the root. For coffee drinkers who are women, the denominator is the number who like coffee.
The next lesson in the collecting data unit is designing questionnaires. Students move from organising given data to writing questions that do not create bias. Keep frequency trees available as the diagram they already trust.
Try this tomorrow. Hide the plenary tree and give only the 120-student travel facts. See who decides that boys and girls, not car, walk and bicycle, must be the first branch.
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