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Frequency trees

Free Printable Frequency trees PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 3)

Download free frequency trees worksheets (PDF), GCSE maths past paper questions and worked solutions for Frequency trees (3Y). This is a Grade 3 probability topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Metatutor and E Classroom, along with past paper question booklets.

Below the worksheet links you can read our frequency trees revision notes and worked examples with diagrams, try real GCSE past paper frequency trees questions with step-by-step solutions, or download a PDF of all frequency trees worksheet links.

Free Frequency trees PDF Worksheets & Answers

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GCSE Maths Grade 3 Revision Notes & Method

Guide to Frequency trees: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A frequency tree organises data by splitting a total group into two categories, and then splitting each branch further. The two branches coming out of any circle must always add up to the number inside that circle.

Work through the clues step by step, filling in any numbers given directly and subtracting from the parent circle to find the partner branch. When asked for a probability at the end, check carefully whether it is out of the whole group or a specific subgroup.

Example 1: 60 students sat a test. 35 are girls. 28 girls passed. In total, 47 students passed. Complete the frequency tree.

60 35 Girls 25 Boys Pass: 28 Fail: 7 Pass: 19 Fail: 6
Boys = 60 − 35 = 25; Girls Fail = 35 − 28 = 7
Boys Pass = 47 − 28 = 19; Boys Fail = 25 − 19 = 6

Example 2: Using the frequency tree from Example 1:
(a) One student is chosen at random. Find P(Boy who failed).
(b) A boy is chosen at random. Find P(Passed).

Solution:

(a) Out of all 60 students, 6 are boys who failed:
P(Boy who failed) = 660 = 110
(b) Out of the 25 boys, 19 passed:
Answer: (a) 660 (or 110)   (b) 1925
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Frequency trees Questions & Answers

Past Paper Example 1 GCSE Nov 2023 3F Q15 5 marks
A travel agent sold 100 holidays in April.
Each of these holidays was in the UK or was abroad.
64 of the 100 holidays were sold to families.
The rest of the holidays were sold to couples.
11 of the 18 holidays abroad were sold to couples.
(a) Use this information to complete the frequency tree. [3 marks]
familiescouplesUKabroadUKabroad100
(b) Find the probability that this holiday was **not** abroad. [2 marks]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
Couples = 36, Couples UK = 36 – 11 = 25 M2
Families abroad = 18 – 11 = 7, Families UK = 64 – 7 = 57 A1
familiescouplesUKabroadUKabroad10064365772511
Answer (a): families = 64 (UK = 57, abroad = 7); couples = 36 (UK = 25, abroad = 11)
Part (b) Solution:
57/64 M1 A1
Answer (b): 5764
Past Paper Example 2 AQA Jun 2022 3F Q9 4 marks
Some students were asked about their daily exercise.
(a) 12 more students answered Yes than answered No.
Complete the frequency tree.
[3 marks]
Total numberof studentsExercisetakenTime exercisingYesNo35At least1 hourLess than1 hour27
(b) One of the 35 students who answered Yes is chosen at random.
What is the probability that they exercise for at least 1 hour?
[1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Yes = 35 M1
Since Yes is 12 more than No: No = 35 - 12 = 23 M1
Total students = 35 + 23 = 58
From 35 Yes students, 27 exercise at least 1 hour, so 35 - 27 = 8 exercise less than 1 hour. A1
Total numberof studentsExercisetakenTime exercisingYesNo583523At least1 hourLess than1 hour278
Answer (a): Answer Total = 58, No = 23, Less than 1 hour = 8
Part (b) Solution:
Out of the 35 students who answered Yes, 27 exercise for at least 1 hour, so probability = 2735. B1
Answer (b): Answer 2735
Past Paper Example 3 GCSE Nov 2019 1F Q15 4 marks
120 people were at a hockey match.
Each person was asked if they wanted to stand or to sit to watch the match.
[INDENT]75 of the people were female
[INDENT]29 of the males wanted to stand
[INDENT]30 of the people wanted to sit
(a) Use this information to complete the frequency tree. [3 marks]
120malefemalesitstandsitstand
(b) Write down the probability that this person is a male who wanted to stand. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Males = 120 – 75 = 45 M1
Male sit = 45 – 29 = 16 M1
Female sit = 30 – 16 = 14
Female stand = 75 – 14 = 61 A1
120malefemalesitstandsitstand457516291461
Answer (a): male=45 (sit=16, stand=29); female=75 (sit=14, stand=61)
Part (b) Solution:
29/120 B1
Answer (b): 29120

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