A supermarket chain has 92000 customers on its loyalty scheme and wants to know how satisfied they are with the delivery service. Which is the best reason for surveying a sample rather than every customer?

Asking all 92000 customers would take too long and cost too much

A sample always gives the same answer as asking everyone

Asking all 92000 customers would take too long and cost too much

A smaller group of people always gives a more accurate result

Ravi wants to find out how often the people of his town use the town library. He stands outside the library one Saturday morning and asks 50 people as they leave. Which statement best explains why his sample is biased?

Everyone he asks already uses the library, so people who never go there had no chance of being chosen

50 people is too small a sample to tell you anything about a town

He should have asked on a weekday rather than a Saturday

He did not ask the same number of men as women

Everyone he asks already uses the library, so people who never go there had no chance of being chosen

Aisha estimates the number of fish in a lake by tagging a first sample of 20 fish. Her teacher suggests repeating the study with a first sample of 200 fish. Which statement best describes the effect of the larger sample?

A larger sample reflects more of the variation in the population, so the estimate should be closer to the true number

A larger sample guarantees that the estimate is exactly right

A larger sample reflects more of the variation in the population, so the estimate should be closer to the true number

A larger sample removes the bias caused by only catching fish near the bank

A larger sample makes no difference, because an estimate from a sample is never any use

Is sampling on the Foundation paper as well as Higher?

No. Spec ref S1 on Edexcel 1MA1, inferring properties of a population from a sample while knowing the limitations of sampling, is Higher tier only. Foundation candidates still collect, represent and interpret data, but the proportional sample calculation and capture-recapture belong to the Higher papers.

How many marks is a stratified sampling question worth?

Usually 2-4 marks. One group taken from a single list is 2 marks, a cell from a two-way table split by two things at once is normally 3, and a part asking for two groups can reach 4. Sampling is not on every paper, so it deserves a short revision slot rather than a long one.

Do you round a stratified sample size up or down?

Round to the nearest whole number, so 9.75 becomes 10 and 13.25 becomes 13. You cannot survey three quarters of a person, and a decimal sitting in the answer box loses the accuracy mark. Round once, at the end: rounding the fraction first is what pushes an answer out by one or two.

Is the capture-recapture formula on the Edexcel formulae sheet?

No. The Exam Aid sheet issued with each 1MA1 paper carries the quadratic formula, the sine and cosine rules, the trapezium and prism formulae, compound interest and the two probability rules, and nothing at all about sampling. Build the calculation from the proportion: the fraction of the second sample that is marked equals the fraction of the whole population that is marked.

Sampling Questions - Edexcel GCSE Higher Maths

Sampling - Edexcel GCSE Higher Maths

Typically 2-4 marks when it appears, and it does not appear on every paper · Spec 1MA1

A population is every member of the group a question is about: all 1240 students at a school, all the fish in a lake, every bolt in a hopper. A sample is the part of it you actually measure. Edexcel files this under spec ref S1 on 1MA1, inferring properties of a population from a sample while knowing the limitations of sampling, and it is Higher tier only. Foundation candidates collect, represent and interpret data; judging whether a sample can carry a conclusion about the population sits on the Higher papers.

Three question types come out of that one line of specification. The commonest is the proportional sample: a college described by year group and gender, a sample of 45 or 50 to be shared out in the same ratio as the population, worth 2-4 marks. Edexcel does not use the word stratified in the 1MA1 subject content, so a question may name it or may simply ask for a sample in proportion, but the arithmetic is identical: group size $\times$ sample size $\div$ population. The second type is capture-recapture, where items are marked, released and partly recaptured, usually 3 marks with a follow-up asking for an assumption. The third is a judgement about a described method: who could not possibly have been picked, and which way that tilts the results. The arithmetic is calculator work, so this fits Papers 2 and 3 most naturally, though figures that divide cleanly would let it appear on Paper 1.

Two habits protect the marks. The final answer counts people, so it must be a whole number, and it must be rounded once, at the very end: an examiner who reads 9.75 in the answer box gives the method mark and stops there. Then read which total the question wants. In a two-way table, 'how many female students are in the sample' uses every female student, not the ones in one row, and what you share out is the sample size, never the population. For capture-recapture, write the proportion in words before touching the calculator: the fraction of the second sample that is marked equals the fraction of the whole population that is marked.

Worked example

A college has 720 students. In Year 12 there are 156 female students and 204 male students. In Year 13 there are 148 female students and 212 male students. Ceri takes a sample of 45 students, stratified by year group and by gender. Work out the number of Year 12 female students and the number of Year 13 male students in her sample.

[4 marks]

Check the population total: $156 + 204 + 148 + 212 = 720$ . The sampling fraction is $\frac{45}{720} = \frac{1}{16}$ , so every group contributes one sixteenth of its members.
M1: sample size over population, kept as a fraction rather than a rounded decimal
Year 12 female students: $156 \times \frac{1}{16} = 9.75$ .
M1: correct product for the first group (156 out of 720, then times 45)
You cannot survey 9.75 people, so round to the nearest whole number: 10 students.
A1: whole number stated; 9.75 alone in the answer box scores nothing here
Year 13 male students: $212 \times \frac{1}{16} = 13.25$ , which rounds to 13 students.
A1: second group correct, this one rounding down; the four groups still total 45

Practice questions

These are original questions in Edexcel 1MA1 Higher style. Nothing is printed as a table here, so each population is written out in words: read for the group you are being asked about and for the total the sample is drawn from. Stratified answers are whole numbers of people, and any question whose answer does not come out exactly says how to round it.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

A supermarket chain has 92000 customers on its loyalty scheme and wants to know how satisfied they are with the delivery service. Which is the best reason for surveying a sample rather than every customer?

Answer options for question 1
A sample always gives the same answer as asking everyone Asking all 92000 customers would take too long and cost too much A smaller group of people always gives a more accurate result A sample cannot be biased
Question 2 Exam pace [4 marks]

A gym has 700 members. 143 are aged under 20, 268 are aged 20 to 39, 189 are aged 40 to 59 and 100 are aged 60 or over. A sample of 40 members, stratified by age group, is taken. Work out how many members aged under 20 and how many aged 60 or over should be in the sample. Give each answer as a whole number.

under 20 = 60 or over =
Question 3 Exam pace [3 marks]

A ranger catches 25 beetles in a garden, marks them and releases them. The next day she catches 40 beetles, and 9 of them are marked. Work out an estimate for the number of beetles in the garden. Give your answer to the nearest whole number.

Your answer (fractions like 1/2 are fine)
Question 4 Exam pace [1 mark]

Ravi wants to find out how often the people of his town use the town library. He stands outside the library one Saturday morning and asks 50 people as they leave. Which statement best explains why his sample is biased?

Answer options for question 4
50 people is too small a sample to tell you anything about a town He should have asked on a weekday rather than a Saturday He did not ask the same number of men as women Everyone he asks already uses the library, so people who never go there had no chance of being chosen
Question 5 Exam pace [3 marks]

A conservationist estimates that a wood contains 500 dormice. She has already fitted tags to 40 of them and released them. She now catches a sample of 75 dormice. Based on her estimate, how many of these 75 would she expect to be tagged?

Your answer (fractions like 1/2 are fine)
Question 6 Exam pace [1 mark]

Aisha estimates the number of fish in a lake by tagging a first sample of 20 fish. Her teacher suggests repeating the study with a first sample of 200 fish. Which statement best describes the effect of the larger sample?

Answer options for question 6
A larger sample guarantees that the estimate is exactly right A larger sample reflects more of the variation in the population, so the estimate should be closer to the true number A larger sample removes the bias caused by only catching fish near the bank A larger sample makes no difference, because an estimate from a sample is never any use

Common mistakes examiners see

Splitting the sample evenly between the groups, so a sample of 50 across three villages becomes $50 \div 3 = 16.7$ and then 17 from each.

Take each group separately: its share of the population, multiplied by the sample size. The largest group must supply the most people. As a check, the group answers should add back to the sample size.
Rounding partway through, or leaving the decimal as the final answer. Both appear in the same question: $\frac{189}{700} \times 40 = 10.8$ gets copied into the answer box, or the multiplier 0.0571 is rounded to 0.06 first and the answer drifts.

One calculation, one rounding. Key in group size $\times$ sample size $\div$ population in a single line, write the decimal down as working, then write the nearest whole number underneath as the answer.
Reading the wrong total from a two-way table: using one cell when the question asks for all the female students in the sample, or quoting a population figure such as 135 when the answer has to be part of a sample of 50.

Before calculating, write down the two numbers you need: the size of the group being asked about and the population total. Then sanity check the answer against the sample size, because no group can supply more people than the whole sample.
Turning the capture-recapture proportion upside down. With 40 marked first and 20 marked in a second sample of 50, $\frac{40 \times 20}{50} = 16$ instead of the correct 100.

Write it as two equal fractions: marked in the second sample over the size of the second sample equals total marked over the population, then cross-multiply. The estimate has to be larger than both samples, so 16 from samples of 40 and 50 is a signal to start again.
Answering 'explain why this sample is biased' with 'the sample is too small'.

Bias is about who could not be chosen, not how many were. Name the excluded group: standing outside a library reaches only people who use the library, and asking 5000 of them rather than 50 would not repair it. Save the size argument for the separate question about why a larger sample gives a better estimate.

Frequently asked questions

Is sampling on the Foundation paper as well as Higher?: No. Spec ref S1 on Edexcel 1MA1, inferring properties of a population from a sample while knowing the limitations of sampling, is Higher tier only. Foundation candidates still collect, represent and interpret data, but the proportional sample calculation and capture-recapture belong to the Higher papers.
How many marks is a stratified sampling question worth?: Usually 2-4 marks. One group taken from a single list is 2 marks, a cell from a two-way table split by two things at once is normally 3, and a part asking for two groups can reach 4. Sampling is not on every paper, so it deserves a short revision slot rather than a long one.
Do you round a stratified sample size up or down?: Round to the nearest whole number, so 9.75 becomes 10 and 13.25 becomes 13. You cannot survey three quarters of a person, and a decimal sitting in the answer box loses the accuracy mark. Round once, at the end: rounding the fraction first is what pushes an answer out by one or two.
Is the capture-recapture formula on the Edexcel formulae sheet?: No. The Exam Aid sheet issued with each 1MA1 paper carries the quadratic formula, the sine and cosine rules, the trapezium and prism formulae, compound interest and the two probability rules, and nothing at all about sampling. Build the calculation from the proportion: the fraction of the second sample that is marked equals the fraction of the whole population that is marked.

Sampling - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics