Population vs Sample Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Population vs Sample.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

In statistics, the population is the entire group of individuals or items you want to study, while the sample is the smaller subset you actually collect data from. We use sample statistics to estimate unknown population parameters.

You want to know the average height of ALL teenagers in your country (population), but you can't measure everyone. So you measure 1000 teenagers (sample) and use that to estimate the whole.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The population is every subject of interest; the sample is the subset actually measured. Statistics from samples estimate (but do not equal) population parameters.

Common stuck point: Students assume a large sample is the same as the full population. Even a 10% sample leaves 90% unmeasured — conclusions require careful inference.

Sense of Study hint: When identifying population vs sample, first ask 'Who or what do I want to draw conclusions about?' — that is the population. Then ask 'Who or what did I actually collect data from?' — that is the sample. Finally, use Greek letters (\mu, \sigma) for population parameters and Latin letters (\bar{x}, s) for sample statistics.

Worked Examples

Example 1

easy
A researcher wants to know the average height of all 16-year-olds in the UK. She measures 500 randomly selected 16-year-olds. Identify the population and sample.

Solution

  1. 1
    Step 1: The population is all 16-year-olds in the UK — this is the entire group of interest.
  2. 2
    Step 2: The sample is the 500 randomly selected 16-year-olds — this is the subset actually measured.
  3. 3
    Step 3: The sample average (statistic) is used to estimate the population average (parameter).

Answer

Population: all UK 16-year-olds. Sample: the 500 selected students.
We use samples because it is usually impractical to measure every member of a population. Random sampling helps ensure the sample is representative.

Example 2

medium
Distinguish between a parameter and a statistic. Give an example of each.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A factory produces 10,000 light bulbs per day. Quality control tests 100 randomly chosen bulbs. Identify the population, sample, and explain why sampling is used.

Example 2

easy
A website wants to know the average time spent on the site by all visitors. It studies 1,200 randomly selected visits from last month. Identify the population, the sample, and the parameter of interest.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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