A population is the complete group a statistical study aims to understand; a sample is the subset of that group actually observed. Researchers use a sample to estimate features of the larger population. Whether those estimates can be generalized depends on how the population is defined and how the sample is covered and selected—not simply on how many people or units are measured.
What do population and sample mean in statistics?
A statistical population is the full set of units relevant to a research question. Units can be people, households, businesses, institutions, or other entities. A sample is a subset of those units selected for observation. Statistics Canada defines a sample as “a subset of the units of a population” and explains that sampling estimates population characteristics by observing part of the group (Statistics Canada glossary).
The distinction is about the study’s scope and what is measured: the population is the group the researcher wants to draw conclusions about, while the sample is the group from which data are collected. A numerical summary calculated from the sample is a sample statistic; it can be used to estimate a corresponding characteristic of the population.
Population vs. sample: a simple example
Suppose a school wants to estimate the average height of its students during the current school year. The population is all students enrolled at the school during that period. If researchers measure 60 selected students, those students form the sample. Their measured average height is a sample statistic used to estimate the average height of all students in the defined population. The estimate is not automatically exact: its usefulness depends on how students were selected and whether the measurements adequately represent the group.
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Define the population before choosing a sample
A population description should be specific enough to show which units a conclusion concerns. Statistics Canada distinguishes the target population—the group about which information is wanted—from the survey population that the survey can actually cover. If practical limits leave some target units out, findings may apply only to the covered survey population; that gap should be disclosed when interpreting results (Statistics Canada, sample selection).
- Units: Who or what is included, such as people, households, or businesses.
- Geography: The places covered.
- Reference period: The time span to which the definition applies.
- Eligibility: Any additional criteria, such as age range or industry.
For example, “students at the school” leaves questions about which school and when. “Students enrolled at North School during the fall term” narrows the units, location, and period; additional eligibility rules may be needed if the study covers only a particular age group or program.
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Sample survey vs. census
A sample survey collects information from some units in a target population and uses those observations to estimate population characteristics. A census seeks information from every unit in the defined population. Neither approach guarantees error-free results; the better fit depends on the question, the required detail, timing, budget, and operational feasibility (Statistics Canada, survey methods).
| Dimension | Sample survey | Census |
|---|---|---|
| Units measured | Some units from the defined population | All units in the defined population are sought |
| Cost and effort | Often lower because fewer units are contacted | Often higher because information is sought from every unit |
| Detail | Can collect detailed data efficiently when the design and sample size support the intended analysis | Can support direct counts and small-subgroup analysis when suitable data are collected |
| Error | Can have sampling error and nonsampling error | Avoids sampling error in the intended all-unit measurement, but can still have nonsampling error |
| Best fit | When estimates of adequate quality meet the need and full enumeration is impractical | When direct counts or detailed coverage are needed and resources and operations permit |
These are tradeoffs, not guarantees. A sample can be biased if parts of the population are poorly covered or selection is unsuitable. A census can still be affected by incomplete coverage, nonresponse, or inaccurate reporting.
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How to judge whether a sample supports a conclusion
- Match the population to the question. Check the units, geography, period, and eligibility criteria. A result about one defined group does not automatically describe a broader or different group.
- Check coverage. Find out how the study identified eligible units and whether its sampling frame omitted relevant parts of the target population. Poor frame coverage can undermine conclusions even when many people respond (Statistics Canada, survey questions).
- Check selection. Look for whether the sample was chosen using a probability-based or non-probability method, and whether the method suits the inference being made. The selection process should be documented; a sample drawn in a way that favors certain units may not represent the full population.
- Consider sample size alongside design. A larger sample is not automatically more representative. Precision needs, selection, coverage, nonresponse, budget, and operating constraints all matter. There is no single minimum size that makes every sample representative.
- Keep the conclusion within the design’s reach. Generalize only to the population the study can adequately support, not to units outside its defined and covered scope.
Sampling error and other sources of error
Sampling error arises because a sample measures only part of a population and uses those observations to estimate a population characteristic. Different samples can produce different estimates. A census avoids sampling error for its intended all-unit measurement, but it is not immune to other problems. Nonsampling errors—such as incomplete coverage, nonresponse, or inaccurate reporting—can affect both sample surveys and censuses (Statistics Canada glossary).
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Common misunderstandings
- “The sample is the population.” No: the sample is the part observed; the population is the full defined group of interest.
- “A bigger sample must be representative.” No: selection bias or missing coverage can distort results regardless of sample size.
- “A census has no errors.” It avoids sampling error in the intended all-unit measurement, but nonsampling errors can remain.
- “A population always means people.” Statistical populations can include households, businesses, institutions, or other defined units.
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