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Mathematics Concept

Sample

A set of observations selected to study a population or process.

Animated scene of an open-air market in Buenos Aires with colorful stalls and people walking.
Properties and conditions
Is interpreted with respect toA population or process
RequiresSelection method
CautionSize and representativeness are different issues

Definition and context

A sample brings together the units we observe within a defined population or process. Its usefulness depends on how they were selected and what question we want to answer. Size matters, but so do coverage and potential biases.

If a hypothetical questionnaire reaches only people who use an application, increasing the number of responses does not guarantee that it describes those who do not use it. This example shows why representativeness requires an explanation of the selection mechanism. We must also identify independent units: many measurements of the same object do not automatically equal many different objects. When reading a study, the description of the sample connects the available data to the actual scope of the conclusions.

What we know and its limits

Introductory reference sheet. Properties and applications depend on measurement conditions; consult the sources before making comparisons.

Follow the evidence

The original sources for exploring this explanation and its limits.

  1. Introductory Statistics 2e · Data and Sampling OpenStax · Rice University
    Samples, bias, and sampling variability.
Image credits

Photo by Agus Paglia on Pexels · Original source · Pexels License

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