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Sampling Methods in ACCA Management Accounting: Random vs Non-Random

Updated 11 October 2026 · Fact-checked

Sampling means studying part of a population to learn about the whole. Random methods (simple random, systematic, stratified, cluster, multistage) give every item a known chance of selection. Non-random methods (quota, convenience, judgemental) do not. To answer a question, match the method to the population, the sampling frame, cost and accuracy needs.

Understand Sampling Methods

A population is every item you want information about, such as all invoices, customers or staff. Checking every item is a census. It is often too slow, too costly, or impossible, for example when testing a product destroys it. So you take a sample: a smaller group chosen from the population.

The sample is chosen from a sampling frame, which is a list of all items in the population. If the frame is incomplete or out of date, the sample can be biased from the start.

Sampling methods split into two families. Random (probability) sampling gives every item a known, non-zero chance of being picked. You can then judge how reliable the results are. Non-random (non-probability) sampling relies on judgement or convenience. It is usually quicker and cheaper, but it can be biased and you cannot measure sampling error in the same way.

The main random methods are:

  • Simple random: every item has an equal chance. Use random number tables or a generator.
  • Systematic: pick a random start, then every kth item, where k = population ÷ sample size.
  • Stratified: split the population into groups (strata) that differ from each other, then sample from each group, usually in proportion to its size.
  • Cluster: split the population into natural groups (clusters), such as branches or regions. Randomly choose some clusters and study all items in them.
  • Multistage: sample in steps. For example, choose regions at random, then stores within those regions, then customers within those stores.

The main non-random methods are:

  • Quota: the interviewer must find a set number of people in each category, such as age band, but picks them by choice.
  • Convenience: use whoever is easy to reach.
  • Judgemental (purposive): the researcher selects items they think are typical or useful.

A useful contrast: stratified and quota sampling both use categories. In stratified sampling the items within each stratum are picked randomly. In quota sampling they are not. Stratified and cluster both use groups. Stratified samples from every group; cluster samples only some groups, then takes everything in them.

Key formulas to remember

Systematic sampling interval
k = population size ÷ sample size
Round sensibly. Choose a random starting point between 1 and k, then select every kth item.
Proportionate stratified sample
Sample from a stratum = (stratum size ÷ population size) × total sample size
Use this when the strata should be represented in proportion to their size. Round to whole items.
Random vs non-random rule
Random = each item has a known, non-zero chance of selection
Quota, convenience and judgemental methods fail this test, so they are non-random.

How to solve Sampling Methods questions

Use this method for any sampling question, whether it asks you to identify a method, choose one, or calculate a sample.

  1. 1Identify the population and whether a sampling frame exists. No frame often rules out true random methods.
  2. 2Read how items are selected. Is chance involved, or does a person choose? Chance means random; personal choice means non-random.
  3. 3Look for groups. If every group is sampled, think stratified or quota. If only some groups are chosen and fully studied, think cluster.
  4. 4Check for steps. Selection in several stages (region, then store, then customer) points to multistage.
  5. 5Check for a fixed interval such as every 20th item. That is systematic.
  6. 6If a calculation is needed, apply the interval or proportion formula and round to whole items.
  7. 7If asked to choose, weigh cost, speed, accuracy, bias and whether a frame is available, then state your pick.
  8. 8Check your answer against the options. Eliminate any that contradict the selection rule.

Quickest way: Three-question shortcut

When to use it: Use for multiple choice questions that describe a sampling scenario and ask you to name the method.

  1. Ask: does chance pick the items? If no, it is non-random (quota if categories with targets, convenience if easy access, judgemental if expert choice).
  2. If yes, ask: is there a fixed interval? If so, it is systematic.
  3. If not, ask how groups are used. All groups sampled means stratified. Some groups, then all items inside, means cluster. Several selection stages means multistage. No groups means simple random.

Common mistakes in Sampling Methods

  • Treating quota sampling as random

    Quota sampling uses categories, just like stratified sampling, so the two look alike.

    Fix: Ask who picks the individual items. If the interviewer chooses, it is quota and non-random.

  • Confusing stratified with cluster sampling

    Both divide the population into groups.

    Fix: Stratified takes some items from every group. Cluster takes all items from some groups.

  • Using the wrong interval in systematic sampling

    Students divide the sample size by the population or forget the random start.

    Fix: Interval = population ÷ sample size. Pick a random start within the first interval.

  • Ignoring the sampling frame

    Students focus on the method name and forget that random methods need a list.

    Fix: State that random methods need a complete, current frame. Without one, consider cluster or non-random methods.

  • Claiming random sampling is always best

    Random sounds more scientific.

    Fix: Weigh cost, time and need for accuracy. Non-random methods can be sensible for quick, low-cost or exploratory work.

  • Not rounding stratum sizes to whole items

    Calculator answers are left as decimals.

    Fix: Round to whole items and check the strata total the required sample size.

Worked examples

Example 1

A company has 2,000 employees: 800 in production, 600 in sales, 400 in administration and 200 in management. It wants a proportionate stratified sample of 100 employees. How many should come from each group?

Show the solution
  1. Sample fraction = 100 ÷ 2,000 = 5%.
  2. Production: 800 × 5% = 40.
  3. Sales: 600 × 5% = 30.
  4. Administration: 400 × 5% = 20.
  5. Management: 200 × 5% = 10.
  6. Check: 40 + 30 + 20 + 10 = 100.

Answer: Production 40, sales 30, administration 20, management 10.

Example 2

A firm has 1,200 invoices numbered 1 to 1,200 and wants a systematic sample of 60. A random start of 7 is chosen. Which invoices are selected first, and what is the last one?

Show the solution
  1. Interval k = 1,200 ÷ 60 = 20.
  2. The first invoice is the random start: 7.
  3. Then add 20 each time: 27, 47, 67 and so on.
  4. The 60th invoice = 7 + (59 × 20) = 7 + 1,180 = 1,187.
  5. Check that 1,187 is within 1 to 1,200. It is.

Answer: Selection starts 7, 27, 47, 67 and the last invoice is number 1,187.

Exam tips

  • Name the method from the selection rule, not from the words in the story. Look for who chooses the items.
  • In multiple response questions, check each option for the same key test: chance or personal choice.
  • For number entry, show the interval or fraction first, then multiply, and check that the strata add up to the total.
  • If asked about advantages, link them to cost, speed, bias and the need for a frame. These are the usual marking points.
  • Remember that quota and stratified are the classic pair to separate, and stratified and cluster are the second.

Practice questions from Sources of data

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.

Sampling Methods: frequently asked questions

What is the difference between random and quota sampling?

In random sampling, chance decides which items are selected, so each has a known chance. In quota sampling, the interviewer must fill set numbers in categories but chooses the people. This makes quota non-random and open to bias.

How is stratified sampling different from cluster sampling?

Stratified sampling divides the population into different groups and samples from every group. Cluster sampling randomly picks some groups and studies all items in them. Stratified aims for accuracy; cluster aims for lower cost.

How do I choose a sampling method in management accounting?

Consider whether a sampling frame exists, the cost and time available, the accuracy needed and the risk of bias. If you need reliable, measurable results and have a frame, use a random method. If speed and low cost matter more, a non-random method may be acceptable.

Why do we sample instead of checking everything?

A full check is often too costly, slow or impossible, for example when testing destroys the item. A well-chosen sample gives useful information at lower cost and effort.