Explain why samples are used, spot bias in how a sample was chosen or a question was worded, and take random or stratified samples. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page.
A sample should represent the population. Bias creeps in when some groups cannot be chosen (phone survey in the day misses workers), the sample is too small, or the question leads the answer. Random sampling gives every member a chance; stratified sampling matches the proportions of groups in the population.
A criticising-the-method question wants a specific flaw and an improvement: 'only asked people at a train station, so car users are missing; ask at several locations or use a random sample from the electoral roll'. Do not write 'it's biased' with no reason.
A census is everyone; a sample is a subset. Leading questions, sampling from the wrong place, and asking only at one time of day all bias the sample. Stratified: each group contributes populationgroup× sample size.
Objectives
The population is everyone you want to know about.
In a simple random sample, every member has an equal chance of being chosen.
Asking only your friends, or only people who walk past one shop at 9am, leaves people out.
Key points
Explain the difference between a population, a sample and a census.
Describe how to take a simple random sample.
Recognise bias in where, when or how a sample was taken, and in leading questions.
Suggest improvements that make a sample more representative.
Worked examples
Example 1
In a random sample of 20 people, 7 own a bike. What percentage of the sample own a bike?
2 marks
Fraction who own a bike = 7/20.
7 ÷ 20 = 0.35.
0.35 × 100 = 35%.
Answer: 35
Common slips
Slip: Fraction who own a bike = 9/20. That changes a number from the question, so it answers a different question.
Slip: 7 × 20 = 140. That uses multiplication, but this step needs division.
Slip: 4.35 × 100 = 35%. That does not match the working above it.
Example 2
A school has 300 students. A random sample of 45 students is taken. What percentage of the students are in the sample?
2 marks
Fraction in the sample = 45/300.
45 ÷ 300 = 0.15.
0.15 × 100 = 15%.
Answer: 15
Common slips
Slip: Fraction in the sample = 47/300. That changes a number from the question, so it answers a different question.
Slip: 45 × 300 = 13500. That uses multiplication, but this step needs division.
Slip: 4.15 × 100 = 15%. That does not match the working above it.
Example 3
In a fair random sample of 40 students, 9 say they like the new menu. The school has 800 students. Estimate how many students in the school like the new menu.
3 marks
The fraction of the sample who like the menu is 9/40.
Use the same fraction for the whole school: 9/40 × 800.
9 ÷ 40 × 800 = 180.
Answer: 180
Common slips
Slip: The fraction of the sample who like the menu is 11/40. That changes a number from the question, so it answers a different question.
Slip: Use the same fraction for the whole school: 12/40 × 800. That changes a number in the working, so the step no longer follows from the one before.
Slip: 13 ÷ 40 × 800 = 180. That does not match the working above it.
Questions and answers
GCSE Maths sampling & bias questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A head teacher wants a random sample of 30 students from a school of 600 students. Which method is best? A: Ask the first 30 students into the canteen. B: Number all 600 students and pick 30 numbers with a random number generator. C: Ask 30 members of the school football team.
Show answer
Answer: B
The population is 600 people.
Method B gives every one of the 600 people an equal chance of being picked.
M1 — The population is 600 people.
A1 — Answer B
Question 2 Easy2 marks
A school has 400 students. A random sample of 28 students is taken. What percentage of the students are in the sample?
Show answer
Answer: 7
Fraction in the sample = 28/400.
28 ÷ 400 = 0.07.
M1 — Fraction in the sample = 28/400.
A1 — Answer 7
Question 3 Medium2 marks
A council wants the views of the 5000 adults in a town. Which method is best? A: Ask people leaving a gym on Monday morning. B: Ask people who reply to a social media post. C: Pick names at random from a list of all the adults in the town.
Show answer
Answer: C
The population is 5000 people.
Method C gives every one of the 5000 people an equal chance of being picked.
M1 — The population is 5000 people.
A1 — Answer C
Question 4 Medium2 marks
In a fair random sample of 40 students, 10 say they like the new menu. The school has 680 students. Estimate how many students in the school like the new menu.
Show answer
Answer: 170
The fraction of the sample who like the menu is 10/40.
Use the same fraction for the whole school: 10/40 × 680.
M1 — The fraction of the sample who like the menu is 10/40.
A1 — Answer 170
Question 5 Hard2 marks
A shop wants a random sample of 20 of its 240 customers who have a loyalty card. Which method is best? A: Give each card number a place in a list and pick 20 using random numbers. B: Ask the first 20 customers on Saturday. C: Ask 20 customers who are buying the most expensive items.
Show answer
Answer: A
The population is 240 people.
Method A gives every one of the 240 people an equal chance of being picked.
M1 — The population is 240 people.
A1 — Answer A
Question 6 Hard2 marks
In a random sample of 50 people, 18 own a bike. What percentage of the sample own a bike?
Show answer
Answer: 36
Fraction who own a bike = 18/50.
18 ÷ 50 = 0.36.
M1 — Fraction who own a bike = 18/50.
A1 — Answer 36
Question 7 Exam-style3 marks
In a fair random sample of 20 students, 6 say they like the new menu. The school has 120 students. Estimate how many students in the school like the new menu.
Show answer
Answer: 36
The fraction of the sample who like the menu is 6/20.
Use the same fraction for the whole school: 6/20 × 120.
6 ÷ 20 × 120 = 36.
M1 — The fraction of the sample who like the menu is 6/20.
M1 — Use the same fraction for the whole school: 6/20 × 120.
A1 — Answer 36
Common mistakes
Most lost marks on this topic are one slip.
Thinking a big sample cannot be biased.
Size does not repair a method that leaves people out.
Choosing people because they are easy to ask.
Convenience is a common source of bias.
Treating a sample percentage as an exact population count.
It is an estimate.
Spot the slip
A biased sample is one where
some of the population are more likely to be picked
the sample is smaller than 30
the results include a decimal
Show the slip
some of the population are more likely to be picked Bias is about the method, not the size alone.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Answer in full sentences that refer to the context: mention the town, the gym, the year groups.
A two-mark 'criticise' question usually wants one problem and one fix — or two different problems if it says 'give two reasons'.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.