A-Level Data Collection

Data collection at A-Level

Before any statistics can be calculated, data has to be collected — and how it's collected determines whether the results can be trusted. This topic covers the vocabulary and methods examiners expect you to use precisely: the difference between a population and a sample, the five named sampling methods, and how to classify the data itself.

Four skills make up this topic:

• Populations and samples — census vs sample, and the sampling frame used to select from
• Sampling methods — simple random, systematic, stratified, quota and opportunity sampling
• Evaluating a sampling method — stating a genuine advantage or disadvantage in context, not a generic list
• Types of data — qualitative vs quantitative, discrete vs continuous, primary vs secondary

Populations, samples and the sampling frame

The population is the entire set of items or individuals under investigation. A census surveys every member of the population; a sample surveys only a smaller, selected part of it. A census gives completely accurate results with no sampling error, but it can be slow, expensive, and often impossible if testing destroys the item (e.g. testing every lightbulb in a batch until it fails). A sample is quicker and cheaper, but its results are only an estimate of the population and are subject to sampling error.

To select a sample, you first need a sampling frame — a list of every sampling unit in the population, usually numbered so units can be selected using random numbers. A sampling unit is a single member of the population available for selection (e.g. one student, one household). A sampling frame is not always identical to the population — a school register may be slightly out of date compared with the actual student population, for example.

Sampling methods

Five named sampling methods are required at A-Level. The first three (simple random, systematic and stratified) are random sampling methods — every selection involves chance, so every sampling unit has a known, non-zero probability of being chosen. Quota and opportunity sampling are non-random — the interviewer's own judgement plays a part in who is actually approached.

Simple random sampling

Every possible sample of the required size has an equal chance of being chosen. In practice: number every unit in the sampling frame, then use a random number generator or random number table to select the required number of units, ignoring any repeat or out-of-range number.

Systematic sampling

Sample members are chosen at a fixed interval, \(k\), through the sampling frame, starting from a randomly chosen point in the first interval. The interval is calculated as \(k = \dfrac{N}{n}\), where \(N\) is the population size and \(n\) is the required sample size.

Stratified sampling

The population is first split into distinct, non-overlapping groups called strata (e.g. year groups, or male/female). A sample is then taken from each stratum, with sample sizes proportional to the size of the stratum, using \(\dfrac{n_h}{n} = \dfrac{N_h}{N}\), so \(n_h = n \times \dfrac{N_h}{N}\). Units within each stratum are then normally selected using simple random sampling.

Quota sampling

The population is divided into groups (e.g. by age or gender), and an interviewer is given a quota — a fixed number to interview from each group — matching the groups' known proportions in the population. Unlike stratified sampling, the interviewer chooses who to approach using their own judgement, so quota sampling is non-random and quick to carry out, but can introduce interviewer bias.

Opportunity (convenience) sampling

The sample is made up of whoever is conveniently available at the time and place of the survey, and who agrees to take part. It requires no sampling frame and is the quickest, cheapest method — but it is highly likely to be biased and unrepresentative, since it depends entirely on who happens to be present.

Types of data

Data is qualitative if it describes a quality or category (e.g. eye colour) and cannot be counted or measured numerically. Data is quantitative if it is numerical. Quantitative data is either discrete — it can only take specific, separate values, usually from counting (e.g. number of siblings: 0, 1, 2, …) — or continuous — it can take any value within a range, limited only by the precision of measurement (e.g. height, time, mass). Data is also classified by its source: primary data is collected first-hand by the person carrying out the investigation; secondary data was already collected by someone else (e.g. published government statistics).

Exam tips

Common mistakes

Practice questions

Work through each question before checking the worked solution.

Core Skills

Exam-Style

A* Challenge

Summary

• A census surveys the whole population; a sample surveys a smaller, selected part of it, chosen from a sampling frame.
• Simple random, systematic and stratified sampling are random methods — every unit has a known chance of selection. Quota and opportunity sampling are non-random — the interviewer's judgement decides who is actually approached.
• Systematic sampling uses a fixed interval \(k = \dfrac{N}{n}\) from a random starting point; stratified sampling allocates \(n_h = n \times \dfrac{N_h}{N}\) to each stratum, then samples within each one at random.
• Data is qualitative (a category) or quantitative (a number); quantitative data is discrete (counted) or continuous (measured).
• Always tie an evaluation of a sampling method to the specific context in the question — vague advantages and disadvantages are not credited.

This is the first topic in Statistics Year 1 (AS). Later topics build directly on the sampling and data classification skills introduced here — particularly when choosing how a dataset was collected before analysing it.

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