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MathidiaMathematics Academy
Data collection and representation
Lesson 42 of 75
Easy practice

Sampling methods

Objective. Compare random, systematic, stratified and opportunity samples.

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Learn: the key idea

Sampling methods are different strategies for selecting a sample from a population, each with strengths and weaknesses for representativeness and practicality. Simple random sampling gives every member an equal chance of selection, often using random number generators; systematic sampling selects every kth member from an ordered list; stratified sampling divides the population into groups (strata) and samples proportionally from each; opportunity sampling simply uses whoever is conveniently available. For example, surveying every 10th customer leaving a shop is systematic sampling, while surveying friends nearby is opportunity sampling and prone to bias. Choosing the right method depends on balancing representativeness, cost, and practicality for the study.

Worked example

A school has 300 boys and 200 girls and wants a sample of 50 students using stratified sampling methods proportional to gender. How many girls should be included?

300 … 200
Illustrated card showing 300 … 200
  1. 1Find the total population: 300 + 200 = 500 students.
  2. 2Find the proportion of girls: 200/500 = 0.4.
  3. 3Multiply by the sample size: 0.4 × 50 = 20.
  4. 4Check: boys would be 0.6 × 50 = 30, and 30 + 20 = 50 matches the sample size.

Answer: 20 girls

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Common mistake. Students often label any convenient method as 'random' even when it is actually opportunity sampling, such as surveying only people passing by. True random sampling requires every member to have an equal, known chance of selection, usually via a formal randomising process.

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