Experiments and frequency Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Experiments and frequency questions. See exactly how to solve problems on frequency tree, completing a frequency tree, missing branch, row total.

frequency treecompleting a frequency treemissing branchrow totaltwo-way tablecompleting a two-way table
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
120120 students took part in a survey about how they travel to school. The students are either girls or boys. Some of the students walk to school and the rest do not walk to school. 7070 of the students are girls. 4545 of the girls walk to school. 3030 of the boys do not walk to school. Complete the frequency tree. Work out how many of the girls do not walk to school.

Worked solution

  1. Write down what you know

    total=120,the number of girls=70,the number of girls who walk to school=45,the number of boys who do not walk to school=30\text{total} = 120, \quad \text{the number of girls} = 70 , \quad \text{the number of girls who walk to school} = 45 , \quad \text{the number of boys who do not walk to school} = 30

    There are 120120 students altogether, and the question gives the number of girls = 7070, the number of girls who walk to school = 4545 and the number of boys who do not walk to school = 3030.

  2. Work out the number of girls who do not walk to school

    the number of girls who do not walk to school=70−45=25\text{the number of girls who do not walk to school} = 70 - 45 = 25

    The counts on the branches out of girls must add back to 7070, so subtract the ones you already know. That gives 70−45=2570 - 45 = 25.

  3. State the answer

    the number of girls who do not walk to school=25\text{the number of girls who do not walk to school} = 25

    So the number of girls who do not walk to school is 2525.

Answer
2525
Question 2
1 markeasy
100100 pupils took part in a survey about a spelling test. The pupils are either boys or girls. Some of the pupils passed the test and the rest did not pass the test. 5050 of the pupils are boys. 3838 of the boys passed the test. 88 of the girls did not pass the test. Complete the frequency tree. Work out how many of the boys did not pass the test.

Worked solution

  1. Write down what you know

    total=100,the number of boys=50,the number of boys who passed the test=38,the number of girls who did not pass the test=8\text{total} = 100, \quad \text{the number of boys} = 50 , \quad \text{the number of boys who passed the test} = 38 , \quad \text{the number of girls who did not pass the test} = 8

    There are 100100 pupils altogether, and the question gives the number of boys = 5050, the number of boys who passed the test = 3838 and the number of girls who did not pass the test = 88.

  2. Work out the number of boys who did not pass the test

    the number of boys who did not pass the test=50−38=12\text{the number of boys who did not pass the test} = 50 - 38 = 12

    The counts on the branches out of boys must add back to 5050, so subtract the ones you already know. That gives 50−38=1250 - 38 = 12.

  3. State the answer

    the number of boys who did not pass the test=12\text{the number of boys who did not pass the test} = 12

    So the number of boys who did not pass the test is 1212.

Answer
1212
Question 3
2 markseasy
120120 students took part in a survey about wearing glasses. The students are either girls or boys. Some of the students wear glasses and the rest do not wear glasses. 6060 of the students are girls. 1818 of the girls wear glasses. 4545 of the boys do not wear glasses. Complete the frequency tree. Work out how many of the girls do not wear glasses.

Worked solution

  1. Write down what you know

    total=120,the number of girls=60,the number of girls who wear glasses=18,the number of boys who do not wear glasses=45\text{total} = 120, \quad \text{the number of girls} = 60 , \quad \text{the number of girls who wear glasses} = 18 , \quad \text{the number of boys who do not wear glasses} = 45

    There are 120120 students altogether, and the question gives the number of girls = 6060, the number of girls who wear glasses = 1818 and the number of boys who do not wear glasses = 4545.

  2. Work out the number of girls who do not wear glasses

    the number of girls who do not wear glasses=60−18=42\text{the number of girls who do not wear glasses} = 60 - 18 = 42

    The counts on the branches out of girls must add back to 6060, so subtract the ones you already know. That gives 60−18=4260 - 18 = 42.

  3. State the answer

    the number of girls who do not wear glasses=42\text{the number of girls who do not wear glasses} = 42

    So the number of girls who do not wear glasses is 4242.

Answer
4242
Question 4
1 markeasy
100100 members took part in a survey at a sports club. The members are either men or women. Some of the members go swimming and the rest do not go swimming. 5050 of the members are men. 2424 of the men go swimming. 2020 of the women do not go swimming. Complete the frequency tree. Work out how many of the members are women.

Worked solution

  1. Write down what you know

    total=100,the number of men=50,the number of men who go swimming=24,the number of women who do not go swimming=20\text{total} = 100, \quad \text{the number of men} = 50 , \quad \text{the number of men who go swimming} = 24 , \quad \text{the number of women who do not go swimming} = 20

    There are 100100 members altogether, and the question gives the number of men = 5050, the number of men who go swimming = 2424 and the number of women who do not go swimming = 2020.

  2. Work out the number of women

    the number of women=100−50=50\text{the number of women} = 100 - 50 = 50

    The row totals must add back to the grand total of 100100, so subtract the row totals you already know. That gives 100−50=50100 - 50 = 50.

  3. State the answer

    the number of women=50\text{the number of women} = 50

    So the number of women is 5050.

Answer
5050
Question 5
2 markseasy
8080 people took part in a survey about owning a pet. The people are either adults or children. Some of the people own a pet and the rest do not own a pet. 6060 of the people are adults. 3535 of the adults own a pet. 88 of the children do not own a pet. Complete the frequency tree. Work out how many of the people are children.

Worked solution

  1. Write down what you know

    total=80,the number of adults=60,the number of adults who own a pet=35,the number of children who do not own a pet=8\text{total} = 80, \quad \text{the number of adults} = 60 , \quad \text{the number of adults who own a pet} = 35 , \quad \text{the number of children who do not own a pet} = 8

    There are 8080 people altogether, and the question gives the number of adults = 6060, the number of adults who own a pet = 3535 and the number of children who do not own a pet = 88.

  2. Work out the number of children

    the number of children=80−60=20\text{the number of children} = 80 - 60 = 20

    The row totals must add back to the grand total of 8080, so subtract the row totals you already know. That gives 80−60=2080 - 60 = 20.

  3. State the answer

    the number of children=20\text{the number of children} = 20

    So the number of children is 2020.

Answer
2020

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