A sample should represent the whole population
What you will learn
Know the rule, then use it
These are the short notes. Read each one, then check you can use it in the worked example below.
Method
Sampling methods: simple random — every member has equal chance, for example lottery
Simple random sampling
Number all 600 students 1–600
Stratified sampling by year group
Find the number per year group
State the key difference
Stratified ensures proportional representation; simple random does not guarantee it
Watch out
Students say 'random is best' without explaining why
Every member of the population should have a fair chance.
sample from each group in proportion to the population.
A school has 600 students. A researcher wants a sample of 60. Compare simple random sampling with stratified sampling by year group.
Simple random sampling: Number all 600 students 1–600. Generate 60 random numbers. Select those students.Advantage: unbiased and each student equally likely. Disadvantage: may not represent year groups proportionally.
Stratified sampling by year group: Find the number per year group.Calculate each year's share of the 60-person sample proportionally.Advantage: guaranteed representation of each year group. Disadvantage: requires a complete list sorted by year group.
State the key difference: Stratified ensures proportional representation; simple random does not guarantee it.
Stratified ensures proportional sub-group representation; simple random may under- or over-sample a group
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
WorkedreasoningA school has 600 students. A researcher wants a sample of 60. Compare simple random sampling with stratified sampling by year group.
3 marks4 minscollecting-and-sampling-data-workedShow solution
A school has 600 students. A researcher wants a sample of 60. Compare simple random sampling with stratified sampling by year group.
- 1.Simple random sampling: Number all 600 students 1–600. Generate 60 random numbers. Select those students.Advantage: unbiased and each student equally likely. Disadvantage: may not represent year groups proportionally.
- 2.Stratified sampling by year group: Find the number per year group.Calculate each year's share of the 60-person sample proportionally.Advantage: guaranteed representation of each year group. Disadvantage: requires a complete list sorted by year group.
- 3.State the key difference: Stratified ensures proportional representation; simple random does not guarantee it.
Stratified ensures proportional sub-group representation; simple random may under- or over-sample a group
- M1: simple random sampling
- M1: stratified sampling by year group
- M1: state the key difference
- A1: Stratified ensures proportional sub-group representation; simple random may under- or over-sample a group
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
DiagnosticrecallGive one advantage of stratified sampling.
1 mark2 minscollecting-and-sampling-data-q1Show solution
Give one advantage of stratified sampling.
- 1.Spot the skill: Sampling methods: simple random — every member has equal chance, for example lottery.
- 2.Use the simple random sampling stage first, then stratified sampling by year group.
- 3.Keep the final answer visible: Ensures all sub-groups are represented proportionally.
Ensures all sub-groups are represented proportionally
- g. lottery. systematic — every nth member from a list. stratified — sample in proportion to sub-groups.cluster — sample whole groups. each has advantages and disadvantages relating to bias, cost and representation.
- A1: Ensures all sub-groups are represented proportionally
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
EasyprocedureWhy might a questionnaire question be biased?
2 marks3 minscollecting-and-sampling-data-q2Show solution
Why might a questionnaire question be biased?
- 1.Spot the skill: Sampling methods: simple random — every member has equal chance, for example lottery.
- 2.Use the stratified sampling by year group stage first, then state the key difference.
- 3.Keep the final answer visible: Leading wording, only offering responses that agree, or not including a 'no' option.
Leading wording, only offering responses that agree, or not including a 'no' option
- g. lottery. systematic — every nth member from a list. stratified — sample in proportion to sub-groups.cluster — sample whole groups. each has advantages and disadvantages relating to bias, cost and representation.
- A1: Leading wording, only offering responses that agree, or not including a 'no' option
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
MediumreasoningWhat is a census?
3 marks4 minscollecting-and-sampling-data-q3Show solution
What is a census?
- 1.Spot the skill: Sampling methods: simple random — every member has equal chance, for example lottery.
- 2.Use the state the key difference stage first, then simple random sampling.
- 3.Keep the final answer visible: Data collected from every member of the population, not a sample.
Data collected from every member of the population, not a sample
- g. lottery. systematic — every nth member from a list. stratified — sample in proportion to sub-groups.cluster — sample whole groups. each has advantages and disadvantages relating to bias, cost and representation.
- A1: Data collected from every member of the population, not a sample
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
Hardproblem solvingSchool has 300 yr10 and 200 yr11 students. A stratified sample of 50 needed. How many from yr10?
3 marks5 minscollecting-and-sampling-data-q4Show solution
School has 300 yr10 and 200 yr11 students. A stratified sample of 50 needed. How many from yr10?
- 1.Spot the skill: Sampling methods: simple random — every member has equal chance, for example lottery.
- 2.Use the simple random sampling stage first, then stratified sampling by year group.
- 3.Keep the final answer visible: 30.
30
- g. lottery. systematic — every nth member from a list. stratified — sample in proportion to sub-groups.cluster — sample whole groups. each has advantages and disadvantages relating to bias, cost and representation.
- A1: 30
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
Exam-stylemulti-stepState the difference between discrete and continuous data.
4 marks6 minscollecting-and-sampling-data-q5Show solution
State the difference between discrete and continuous data.
- 1.Spot the skill: Sampling methods: simple random — every member has equal chance, for example lottery.
- 2.Use the stratified sampling by year group stage first, then state the key difference.
- 3.Keep the final answer visible: Discrete takes exact countable values; continuous can take any value in a range.
Discrete takes exact countable values; continuous can take any value in a range
- g. lottery. systematic — every nth member from a list. stratified — sample in proportion to sub-groups.cluster — sample whole groups. each has advantages and disadvantages relating to bias, cost and representation.
- A1: Discrete takes exact countable values; continuous can take any value in a range
Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
Grade 9 stretchproblem solvingA year group contains 180 girls and 120 boys. A stratified sample has size 50. How many girls should be selected?
4 marks7 minssampling-g9Show solution
A year group contains 180 girls and 120 boys. A stratified sample has size 50. How many girls should be selected?
- 1.Find the proportion of girls.
- 2.Multiply the proportion by the sample size.
30 girls
- M1: use × 50
- A1: 30
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Collecting and sampling data - 2 marksGive one advantage of stratified sampling.Mark answer
Ensures all sub-groups are represented proportionally
2Averages and range - 2 marksFind the mean of: 6, 6, 7, 9, 12.Mark answer
8
3Grouped data and estimated mean - 2 marksWhich class contains the median for 30 values with frequencies 8, 12, 10?Mark answer
The 15th and 16th values — both in the second class [frequency 8, then 8+12=20]
4Charts, tables and diagrams - 3 marksA back-to-back stem-and-leaf shows boys' scores and girls' scores. How do you compare distributions?Mark answer
Compare medians and ranges for each group
- I can explain the method for collecting and sampling data.
- I can show clear working without skipping key steps.
- I can avoid this mistake: Students say 'random is best' without explaining why.Marks come from the trade-off: what does each method guarantee, and at what cost?Always give both an advantage and a disadvantage for each method asked.
This guide follows the Pearson Edexcel GCSE Mathematics 1MA1 specification. Practice questions are original Learnova questions shaped around official content and exam skills.