Data Collection: Sampling Methods

What you'll learn

Sampling is a fundamental data collection technique used when studying an entire population is impractical or impossible. This revision guide covers the sampling methods required for AQA GCSE Statistics, explaining when and how to use each technique effectively. You'll learn to identify appropriate sampling methods, calculate sample sizes for stratified sampling, and evaluate the advantages and disadvantages of each approach.

Key terms and definitions

Population — the entire group of individuals or items being studied

Sample — a subset of the population selected for investigation, used to make inferences about the whole population

Sampling frame — a complete list of all members of the population from which a sample can be selected

Sampling unit — an individual member of the population that could be selected for the sample

Bias — systematic favouring of certain outcomes or members of the population, which makes the sample unrepresentative

Random sampling — a method where every member of the population has a known, non-zero probability of being selected

Stratified sampling — dividing the population into distinct groups (strata) and sampling proportionally from each group

Quota sampling — a non-random method where the interviewer selects a specified number of people from different categories

Core concepts

Why we use sampling

In most real-world scenarios, collecting data from an entire population is impossible due to time, cost, or practical constraints. For example:

• Testing every light bulb a factory produces would leave none to sell
• Surveying every student in the UK about exam stress would take years
• Measuring pollution levels at every point in a river is physically impossible

Sampling allows researchers to gather reliable information about a population by studying a smaller, manageable group. The key is ensuring the sample accurately represents the population.

Census refers to collecting data from the entire population. While more accurate, a census is only practical for small populations or when complete accuracy is essential (such as the UK National Census every ten years).

Simple random sampling

In simple random sampling, every member of the population has an equal chance of being selected. This is the fairest method and eliminates selection bias when implemented correctly.

How to conduct simple random sampling:

1. Obtain a complete sampling frame (numbered list of all population members)
2. Use a random number generator or random number table to select sample members
3. Match the random numbers to members of the sampling frame

Example: To select 30 students from a school year of 180 students, number all students 1-180, then use a random number generator to produce 30 different numbers between 1 and 180.

Advantages:

• Free from bias
• Easy to understand and implement
• Each member has a known probability of selection
• Results can be generalized to the population

Disadvantages:

• Requires a complete sampling frame (not always available)
• May not reflect the population structure if sample size is small
• Can be impractical for large, geographically spread populations
• May by chance produce an unrepresentative sample

Systematic sampling

Systematic sampling involves selecting members at regular intervals from an ordered sampling frame. This method is often easier to implement than simple random sampling.

How to conduct systematic sampling:

1. Obtain a sampling frame and number all members
2. Calculate the sampling interval: k = population size ÷ sample size
3. Select a random starting point between 1 and k
4. Select every kth member from that point onwards

Example: To select 40 students from 360 students, calculate k = 360 ÷ 40 = 9. Choose a random start number between 1 and 9 (say, 5), then select students numbered 5, 14, 23, 32, 41, and so on.

Advantages:

• Simple and quick to conduct
• Works well with large populations
• More practical than simple random sampling for geographically spread populations
• Ensures even coverage across the sampling frame

Disadvantages:

• Requires a complete sampling frame
• Can introduce bias if the sampling frame has a periodic pattern (e.g., selecting every 7th day of the week would always give the same day)
• Not truly random as not all combinations of members can be selected
• Once the first member is chosen, all others are predetermined

Stratified sampling

Stratified sampling is used when the population has distinct subgroups (strata) that differ in important ways. Each stratum is sampled proportionally to its size in the population, ensuring representation of all groups.

How to conduct stratified sampling:

1. Divide the population into non-overlapping strata (e.g., by age, gender, year group)
2. Calculate the proportion each stratum represents in the population
3. Calculate how many members should be sampled from each stratum:
   • Sample from stratum = (stratum size ÷ population size) × total sample size
4. Use random sampling within each stratum to select the required number

Example: A school has 600 students: 200 in Year 10, 250 in Year 11, and 150 in Year 12. To select a stratified sample of 60 students:

• Year 10: (200 ÷ 600) × 60 = 20 students
• Year 11: (250 ÷ 600) × 60 = 25 students
• Year 12: (150 ÷ 600) × 60 = 15 students

Advantages:

• Guarantees representation of all important subgroups
• More representative than simple random sampling for heterogeneous populations
• Can make valid comparisons between strata
• Reduces sampling variability

Disadvantages:

• Requires detailed information about the population structure
• More complex and time-consuming than simple methods
• Classification into strata can be difficult or subjective
• Requires a sampling frame for each stratum

Quota sampling

Quota sampling is a non-random method where interviewers select people to meet predetermined quotas for different categories. Unlike stratified sampling, selection within quotas is non-random.

How to conduct quota sampling:

1. Divide the population into categories based on characteristics (e.g., age, gender)
2. Set quotas for each category, often proportional to the population
3. Interviewers select members who fit each category until quotas are filled
4. Selection is at the interviewer's discretion (often convenience-based)

Example: A market researcher needs 100 shoppers: 40 male, 60 female. They stand in a shopping centre and approach people until they have interviewed exactly 40 men and 60 women.

Advantages:

• Quick and inexpensive to administer
• No sampling frame required
• Practical for street surveys and market research
• Ensures representation of key groups

Disadvantages:

• Non-random selection introduces bias (interviewer may unconsciously select certain types of people)
• Cannot generalize findings to the population with statistical confidence
• Interviewers may fill quotas with easily accessible people
• No control over selection within categories

Opportunity (convenience) sampling

Opportunity sampling involves selecting members who are readily available or convenient to access. This is the weakest sampling method and is highly prone to bias.

Example: Surveying only students in your own class about homework preferences, or asking people in one location at one time.

Why it's problematic:

• Highly unrepresentative
• Introduces severe selection bias
• Cannot generalize findings
• Only acceptable when no other method is feasible

At GCSE level, you should be able to identify this method and explain why it produces biased results.

Worked examples

Example 1: Calculating stratified sample sizes

Question: A youth club has 150 members: 45 aged 11-13, 60 aged 14-15, and 45 aged 16-18. The organizers want to survey 50 members using stratified sampling by age group. Calculate how many members should be selected from each age group. (3 marks)

Solution:

For ages 11-13: (45 ÷ 150) × 50 = 0.3 × 50 = 15 members ✓

For ages 14-15: (60 ÷ 150) × 50 = 0.4 × 50 = 20 members ✓

For ages 16-18: (45 ÷ 150) × 50 = 0.3 × 50 = 15 members ✓

Mark scheme: 1 mark for correct method (showing division by population total and multiplication by sample size), 1 mark for two correct values, 1 mark for all three correct values.

Example 2: Describing systematic sampling

Question: Explain how you would use systematic sampling to select 25 members from a fitness club with 400 members. (3 marks)

Solution:

• Calculate the sampling interval: k = 400 ÷ 25 = 16 ✓
• Select a random starting point between 1 and 16 ✓
• Select every 16th member from the numbered list of all 400 members ✓

Mark scheme: 1 mark for calculating correct sampling interval, 1 mark for random start, 1 mark for selecting at regular intervals.

Example 3: Identifying bias and suggesting improvements

Question: A restaurant manager wants to know customer satisfaction. She asks the first 20 customers who arrive on Monday lunchtime to complete a survey.

(a) Give two reasons why this sample may be biased. (2 marks) (b) Suggest a better sampling method and explain why. (2 marks)

Solution:

(a)

• Monday lunchtime customers may not represent customers at other times/days (e.g., weekend evening customers) ✓
• The first 20 customers to arrive may differ from later customers in systematic ways (e.g., early lunch-goers may be retired people, not representing workers) ✓

(b)

• Use systematic sampling by selecting every nth customer across different days and times ✓
• This would ensure representation of customers throughout the week and at different meal times, reducing bias ✓

Alternative acceptable answer for (b): Stratified sampling by dividing customers into lunch/dinner and weekday/weekend groups, then sampling proportionally from each.

Common mistakes and how to avoid them

• Confusing stratified and quota sampling — Remember: stratified sampling uses random selection within each stratum; quota sampling relies on non-random, convenience-based selection by the interviewer.

• Incorrect stratified sample calculations — Always divide the stratum size by the total population size first, then multiply by the desired sample size. Show your working: (stratum ÷ population) × sample size.

• Forgetting to specify random selection in systematic sampling — The starting point must be chosen randomly; otherwise the sample is not representative. Always mention this in exam answers.

• Not checking stratified samples add up — After calculating individual strata samples, verify they sum to the total sample size. If they don't due to rounding, adjust appropriately.

• Assuming all sampling methods are equally valid — Different methods suit different situations. Opportunity sampling is almost never appropriate for drawing reliable conclusions; examiners expect you to criticize it.

• Failing to link disadvantages to context — When discussing limitations, relate them to the specific scenario in the question rather than listing generic disadvantages.

Exam technique for "Data Collection: Sampling Methods"

• Command word "Describe" requires you to explain the step-by-step process (typically worth 2-3 marks). Include: obtaining a sampling frame, how selection occurs, and specific details like calculating intervals or using random numbers.

• Command word "Explain" needs justification, not just description. Link your answer to advantages (representativeness, reduced bias) or disadvantages (time, cost, requires sampling frame) relevant to the context.

• Calculation questions for stratified sampling — always show the formula (stratum size ÷ population size) × sample size for full marks. Examiners award method marks even if your arithmetic is wrong.

• Evaluation questions — discuss both advantages and disadvantages unless the question specifies otherwise. Use the context: a school scenario is different from a national survey in terms of practicality and available resources.

Quick revision summary

Sampling selects a subset of the population for practical data collection. Simple random sampling gives each member equal probability of selection using random numbers. Systematic sampling selects every kth member after a random start. Stratified sampling divides the population into groups and samples proportionally from each, calculated as (stratum size ÷ population size) × sample size. Quota sampling sets non-random quotas for categories. Each method has specific advantages (representativeness, practicality) and disadvantages (bias, requiring sampling frames, complexity) that you must evaluate in context.