Sampling Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Sampling questions. See exactly how to solve problems on sample proportion, simplifying fractions, fraction to percentage, scaling up to a population.

sample proportionsimplifying fractionsfraction to percentagescaling up to a populationestimationbias
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
In a random sample of 3030 students at Ashfield School, 1212 walk to school. Write the proportion of the sample that walk to school as a fraction in its simplest form.

Worked solution

  1. Write down the two numbers you need

    12 out of 3012 \text{ out of } 30

    1212 of the students in the sample walk to school, out of 3030 students altogether.

  2. Write the proportion as a fraction

    1230\frac{12}{30}

    The proportion is the number in the group you want over the total size of the sample, so it is 1230\frac{12}{30}.

  3. Simplify the fraction

    1230=25\frac{12}{30} = \frac{2}{5}

    The highest common factor of 1212 and 3030 is 66, so divide top and bottom by 66 to get 25\frac{2}{5} in its simplest form.

Answer
25\frac{2}{5}
Question 2
1 markeasy
In a random sample of 2424 pupils at Northgate School, 99 have a school dinner. Write the proportion of the sample that have a school dinner as a fraction in its simplest form.

Worked solution

  1. Write down the two numbers you need

    9 out of 249 \text{ out of } 24

    99 of the pupils in the sample have a school dinner, out of 2424 pupils altogether.

  2. Write the proportion as a fraction

    924\frac{9}{24}

    The proportion is the number in the group you want over the total size of the sample, so it is 924\frac{9}{24}.

  3. Simplify the fraction

    924=38\frac{9}{24} = \frac{3}{8}

    The highest common factor of 99 and 2424 is 33, so divide top and bottom by 33 to get 38\frac{3}{8} in its simplest form.

Answer
38\frac{3}{8}
Question 3
2 markseasy
In a random sample of 4545 adults in the town of Marston, 1818 own a car. Write the proportion of the sample that own a car as a fraction in its simplest form.

Worked solution

  1. Write down the two numbers you need

    18 out of 4518 \text{ out of } 45

    1818 of the adults in the sample own a car, out of 4545 adults altogether.

  2. Write the proportion as a fraction

    1845\frac{18}{45}

    The proportion is the number in the group you want over the total size of the sample, so it is 1845\frac{18}{45}.

  3. Simplify the fraction

    1845=25\frac{18}{45} = \frac{2}{5}

    The highest common factor of 1818 and 4545 is 99, so divide top and bottom by 99 to get 25\frac{2}{5} in its simplest form.

Answer
25\frac{2}{5}
Question 4
1 markeasy
In a random sample of 3636 members at Riverside Sports Club, 1515 play tennis. Write the proportion of the sample that play tennis as a fraction in its simplest form.

Worked solution

  1. Write down the two numbers you need

    15 out of 3615 \text{ out of } 36

    1515 of the members in the sample play tennis, out of 3636 members altogether.

  2. Write the proportion as a fraction

    1536\frac{15}{36}

    The proportion is the number in the group you want over the total size of the sample, so it is 1536\frac{15}{36}.

  3. Simplify the fraction

    1536=512\frac{15}{36} = \frac{5}{12}

    The highest common factor of 1515 and 3636 is 33, so divide top and bottom by 33 to get 512\frac{5}{12} in its simplest form.

Answer
512\frac{5}{12}
Question 5
2 markseasy
In a random sample of 2525 households in the village of Denby, 77 have a pet. Work out the percentage of the sample that have a pet.

Worked solution

  1. Write the sample result as a fraction

    725\frac{7}{25}

    77 of the 2525 households in the sample have a pet, so the proportion is 725\frac{7}{25}.

  2. Multiply by 100 to get a percentage

    0.28×100=28%0.28 \times 100 = 28\%

    A percentage is a proportion out of 100100, so multiply by 100100: 28%28\% of the sample have a pet.

  3. State the answer

    28%28\%

    28%28\% of the sample have a pet. Because this comes from a sample it is only an estimate of the percentage in the whole population.

Answer
28%28\%

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