Frequency trees Quiz (Grade 3)

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Score: 0 / 10

Frequency trees — Notes & Worked Examples Show / Hide

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.

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

One Page Guide (PDF) Frequency trees Worksheets

Question 1

[2 marks]

There are 91 students in Year 7.
48 of them are boys.
29 boys walk to school.
26 girls take the bus.
(a) Complete the frequency tree.
(b) A person is chosen at random. Find the probability they are a girl who take the bus.
(c) A boy is chosen at random. Find the probability they walk to school.

Worked Solution & Answer

Probability = successful outcomestotal possible outcomes (all mutually exclusive outcomes add up to 1).
(b) 27 (c) 2948

Answer: (b) 27 (c) 2948

Question 2

[2 marks]

There are 120 people visit a centre.
90 of them are adults.
30 adults go swimming.
11 children use the gym.
(a) Complete the frequency tree.
(b) A person is chosen at random. Find the probability they are a child who use the gym.
(c) An adult is chosen at random. Find the probability they go swimming.

Worked Solution & Answer

Probability = successful outcomestotal possible outcomes (all mutually exclusive outcomes add up to 1).
(b) 11120 (c) 13

Answer: (b) 11120 (c) 13

Question 3 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]

(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]

Answer

Worked Solution & Answer

(a)

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

Answer (a): Answer Total = 58, No = 23, Less than 1 hour = 8

(b)

Out of the 35 students who answered Yes, 27 exercise for at least 1 hour, so probability = 2735. B1

Answer (b): Answer 2735

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[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]

(b) Write down the probability that this person is a male who wanted to stand. [1 mark]

Worked Solution & Answer

(a)

Males = 120 – 75 = 45 M1
Male sit = 45 – 29 = 16 M1
Female sit = 30 – 16 = 14
Female stand = 75 – 14 = 61 A1

Answer (a): male=45 (sit=16, stand=29); female=75 (sit=14, stand=61)

(b)

29/120 B1

Answer (b): 29120

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[4 marks]

120 students are asked if they have a skateboard or a scooter.
37 of the students have a skateboard.
21 of the students who have a skateboard also have a scooter.
65 of the students have a scooter.

(a) Use this information to complete the frequency tree. [3 marks]

(b) Find the probability that this student does not have a skateboard. [1 mark]

Worked Solution & Answer

(a)

Skateboard = 37 ⇒ No skateboard = 120 – 37 = 83 M1
Skateboard & Scooter = 21 ⇒ Skateboard & No scooter = 37 – 21 = 16 M1
Total scooter = 65 ⇒ No skateboard & Scooter = 65 – 21 = 44
No skateboard & No scooter = 83 – 44 = 39 A1

Answer (a): Tree completed (37, 83; 21, 16, 44, 39)

(b)

83/120 B1

Answer (b): 83120

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 AQA Nov 2020 3F Q9

[5 marks]

500 people started a race.
280 were men and the rest were women.
80% of the men finished the race.
30 women did not finish the race.

Complete the frequency tree.

Worked Solution & Answer

Women = 500 - 280 = 220 M1
Men who finished = 0.80 × 280 = 224 M1
Men who did not finish = 280 - 224 = 56 M1
Women who finished = 220 - 30 = 190 M1
Women who did not finish = 30 A1

Answer: Men: 280, Women: 220, Men Finished: 224, Men Not Finished: 56, Women Finished: 190, Women Not Finished: 30

Question Paper (PDF) • Mark Scheme (PDF)

Question 7

[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]

(b) Find the probability that this holiday was **not** abroad. [2 marks]

Worked Solution & Answer

(a)

Couples = 36, Couples UK = 36 – 11 = 25 M2
Families abroad = 18 – 11 = 7, Families UK = 64 – 7 = 57 A1

Answer (a): families = 64 (UK = 57, abroad = 7); couples = 36 (UK = 25, abroad = 11)

(b)

57/64 M1 A1

Answer (b): 5764

Question Paper (PDF) • Mark Scheme (PDF)

Question 8

[5 marks]

200 people live in a village.
23 people do **not** have a garden.
10 males do **not** have a garden.
95 people are male.

(a) Use this information to complete the frequency tree. [3 marks]

(b) Write down the probability that this person is female. [2 marks]

Worked Solution & Answer

(a)

No garden female = 23 – 10 = 13 M1
Garden total = 200 – 23 = 177 M1
Garden male = 95 – 10 = 85
Garden female = 177 – 85 = 92 A1

Answer (a): No garden = 23 (male 10, female 13); Garden = 177 (male 85, female 92)

(b)

13/23 M1 A1

Answer (b): 1323

Question Paper (PDF) • Mark Scheme (PDF)

Question 9

[5 marks]

80 people are asked if they like coffee.
48 of these people are women.
61 of the 80 people like coffee.
8 of the men do **not** like coffee.

(a) Use this information to complete the frequency tree. [3 marks]

(b) Find the probability that this person is a woman. [2 marks]

Worked Solution & Answer

(a)

Men = 80 – 48 = 32 M1
Men like = 32 – 8 = 24 M1
Women like = 61 – 24 = 37
Women do not = 48 – 37 = 11 A1

Answer (a): Men = 32 (like = 24, do not = 8); Women = 48 (like = 37, do not = 11)

(b)

37/61 M1 A1

Answer (b): 3761

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 AQA Nov 2024 1F Q7

[6 marks]

120 people visit a maze.
80 are children, the rest are adults.
At the start of the maze you can turn left or right.
45 children turn left.
75 people in total turn left.

(a) Complete the frequency tree. [4 marks]

(b) What fraction of the **children** turn left?
Give your answer in its simplest form. [2 marks]

Answer

Worked Solution & Answer

(a)

Adults = 120 - 80 = 40 M1
Children right = 80 - 45 = 35 M1
Adults left = 75 - 45 = 30 M1
Adults right = 40 - 30 = 10 A1

Answer (a): Children = 80 (Left = 45, Right = 35); Adults = 40 (Left = 30, Right = 10)

(b)

4580 = 916 M1 A1

Answer (b): Answer 916

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 42 marks)

Frequency trees Worksheets Next: Two way tables →

Grade 3 Quizzes

24 Topics

3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables