Management Accounting · Sampling methods

Random Sampling Methods for ACCA Management Accounting

Updated 11 October 2026 · Fact-checked

Random sampling methods select a sample so that every item has a known chance of being chosen. The four you need are simple random, systematic, stratified and multistage. To answer a question, identify the sampling frame, apply the stated selection rule, and match the method to its features.

Understand Random Sampling Methods

A sample is a part of a population that you study to learn about the whole. You use it because checking every item costs too much or takes too long. In random (probability) sampling, every item has a known, non-zero chance of selection. This lets you measure sampling error and avoid selection bias.

To sample, you need a sampling frame. This is a list of every item in the population, such as a customer list or an invoice file. Most random methods need a frame.

Simple random sampling: every item has an equal chance of being chosen, and every possible sample of the same size is equally likely. You number the items in the frame, then pick numbers using random number tables or a computer generator. It is fair and simple, but it needs a full frame and can miss small groups by chance.

Systematic sampling: you pick a random starting point, then take every kth item. The interval k = population size ÷ sample size. It is quick and easy, but it can give a biased sample if the list has a regular pattern that matches the interval, for example every 7th day always being a Sunday.

Stratified sampling: you split the population into groups (strata) that differ from each other, such as departments or product lines. Then you take a random sample from each stratum, usually in proportion to its size. Each group is represented, and the result is more precise. The cost is that you must know the strata and have a frame for each.

Multistage sampling: you sample in steps. For example, you pick regions at random, then towns within those regions, then customers within those towns. You need a frame only for the units at each stage, not for the whole population, so it saves cost on spread-out populations. It carries more sampling error than a simple random sample of the same size.

Exam questions often contrast stratified with cluster sampling. In stratified sampling, you sample from every group, and the groups are different from one another. In cluster sampling, you select some groups at random and study items within the chosen groups only, and the groups are each a small copy of the population. Multistage sampling often uses clusters as its early stages.

Key formulas to remember

Sampling interval (systematic): k = population size ÷ sample size; Round down to a whole number if needed. Choose a random start between 1 and k, then add k each time.
Proportionate stratified sample: Stratum sample = (stratum size ÷ population size) × total sample size; Round to whole items and check that the strata samples add up to the total sample size.
Simple random selection rule: Chance of selecting each item = sample size ÷ population size; Applies when all items have an equal chance. Ignore repeated numbers if sampling without replacement.

How to solve Random Sampling Methods questions

Use this method for any question on random sampling, whether it asks you to choose a method or to carry one out.

1Read what the question gives you: population size, sample size, whether a list exists, and whether there are distinct groups.
2Name the method asked for, or pick the one that matches the features described.
3For simple random, number the frame, then take numbers from the tables or generator. Skip numbers outside the range and repeats.
4For systematic, work out k = population ÷ sample size, pick a random start from 1 to k, then add k each time.
5For stratified, compute each stratum's share of the population and multiply by the sample size. Round and check the total.
6For multistage, list the stages in order and state what is chosen at each stage.
7Check that the answer is a whole number of items and that the sample size is exactly as required.
8If asked for a reason, link it to a feature: frame needed, bias risk, cost, or representation of groups.

Quickest way: Match the clue to the method

When to use it: Use this on multiple choice questions where you have to pick the method or spot its weakness.

Equal chance for all and random number tables: simple random.
Every kth item or random start with a fixed interval: systematic.
Separate groups, each sampled: stratified.
Groups chosen at random, then sampling within them: cluster or multistage.
Steps through regions, then towns, then people: multistage.
Pattern in the list matching the interval: bias risk in systematic.
No full list available: multistage avoids needing a complete frame.

Common mistakes in Random Sampling Methods

Treating stratified and cluster sampling as the same.
Both split the population into groups.
Fix: Stratified samples from every group. Cluster samples only from some groups chosen at random.
Using a fixed start such as item 1 in systematic sampling.
It looks simpler.
Fix: Choose the start at random from 1 to k, otherwise the sample is not truly random.
Not checking that stratum samples add up to the total.
Rounding each stratum separately.
Fix: Add up the rounded figures and adjust the largest stratum if the total is off.
Saying systematic sampling is always biased.
Remembering the pattern warning too broadly.
Fix: Bias arises only when the list has a pattern that matches the interval. Otherwise it behaves much like simple random.
Calling any quick or convenient sample random.
Confusing random with haphazard.
Fix: Random means each item has a known chance of selection. Choosing whoever is nearby is non-random.
Using the sample size instead of the population size to find the interval.
Mixing up the two numbers under time pressure.
Fix: Always divide the population by the sample size.

Worked examples

Example 1

A company has 2,400 invoices in a numbered file. The auditor wants a systematic sample of 60 invoices and picks a random start of 17. Find the interval, the first four invoices chosen, and the last invoice chosen.

Show the solution

Interval k = 2,400 ÷ 60 = 40.
The start is 17, which lies between 1 and 40, so it is valid.
First four invoices: 17, 17 + 40 = 57, 97, 137.
The nth invoice is 17 + 40 × (n − 1). For n = 60: 17 + 40 × 59 = 17 + 2,360 = 2,377.
Check: 2,377 is no more than 2,400, so it is within the file.

Answer: Interval is 40. The first four invoices are 17, 57, 97 and 137. The last invoice chosen is 2,377.

Example 2

A firm has 500 employees: 200 in production, 150 in sales, 100 in administration and 50 in finance. It wants a proportionate stratified sample of 50 employees for a survey. How many should it select from each department, and how is each chosen?

Show the solution

Sampling fraction = 50 ÷ 500 = 1/10.
Production: 200 × 1/10 = 20.
Sales: 150 × 1/10 = 15.
Administration: 100 × 1/10 = 10.
Finance: 50 × 1/10 = 5.
Check: 20 + 15 + 10 + 5 = 50, which equals the required sample.
Within each department, select the employees by simple random sampling from that department's list.

Answer: Select 20 from production, 15 from sales, 10 from administration and 5 from finance, each chosen randomly within the department.

Exam tips

Learn one clue phrase for each method, so you can match a scenario to it in seconds.
In number entry questions on sampling, calculate carefully and check that the total equals the sample size.
When asked for an advantage or a weakness, tie it to a specific feature such as frame needed, pattern risk, cost or group representation.
In multiple response questions, read the number you must select and test each statement against the method's definition.
Watch the word random: methods based on convenience or judgement are non-random and belong to a different topic.

Practice questions from Sampling methods

Random Sampling Methods in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Actuarial Core Principles (IAI)Population, Sample and Random Sampling

Random Sampling Methods: frequently asked questions

What is the difference between stratified and cluster sampling?

In stratified sampling you divide the population into different groups and sample from every group. In cluster sampling you select some groups at random and sample only within those. Strata are meant to differ from each other, while clusters are meant to look like the whole population.

How do you do systematic sampling with an example?

Divide the population by the sample size to get the interval k. Pick a random start from 1 to k, then take every kth item. With 1,000 items and a sample of 50, k = 20. If the start is 6, you pick items 6, 26, 46 and so on.

How do random number tables work in simple random sampling?

You number every item in the frame, then read digits from the table in groups matching the number of digits in the population size. You ignore numbers outside the range and repeats. You continue until you have the required sample size.

What is multistage sampling in ACCA?

It is sampling in several steps, each from the units chosen in the step before. An example is regions, then towns, then households. It reduces the need for a full frame and cuts travel cost, but it adds sampling error.