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MathidiaMathematics Academy
Data collection and representation
Lesson 41 of 75
Introduction

Populations and samples

Objective. Distinguish populations, samples and sampling units.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A population is the entire group being studied, while a sample is a smaller subset actually selected and measured, used to draw conclusions about the whole population when studying everyone is impractical. Each individual unit of the population from which a sample can be drawn is called a sampling unit, and a complete list of these units is called a sampling frame. For example, to study the heights of all Year 12 students in England, the population is every Year 12 student, and a sample might be 200 students chosen from several schools. Choosing a representative sample matters because conclusions drawn from a biased sample may not generalise to the whole population.

Worked example

A researcher wants to know the average screen time of all teenagers in the UK, so she surveys 150 teenagers from three cities. Identify the population and the sample in this study.

150
Illustrated card showing 150
  1. 1The population is the group the researcher wants to know about: all teenagers in the UK.
  2. 2The sample is the smaller group actually measured: the 150 teenagers surveyed.
  3. 3Check the sample is a subset of the population, which it is since surveyed teenagers belong to the UK teenage population.
  4. 4State both clearly as the final answer.

Answer: Population: all UK teenagers; sample: the 150 teenagers surveyed

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Common mistake. Students often call a large group a 'sample' simply because it is big, forgetting that size alone does not define a sample; what matters is whether it is a genuine subset selected from the full population being studied.

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