Population

Population

A population is the complete set of observations that a researcher wants to learn about. A population includes all of the individuals, objects, events, or cases that could potentially be studied for a particular question.

Examples of Populations

Depending on the research question, a population might be:

  • All students at a particular school

  • All voters in a state

  • All cars produced by a manufacturer this year

  • All games played by a sports team during a season

The population is defined by the question being asked.

Population vs. Sample

Because it is often difficult or impossible to study every member of a population, researchers usually collect data from a sample.

Term

Description

Population

The complete set of observations of interest

Sample

The subset of observations that are actually studied

For example:

  • Population: All students in a school district

  • Sample: 500 students selected from that district

Researchers use information from the sample to learn about the population.

Populations and the Data-Generating Process

In a modeling approach to statistics, it is often useful to think about a population as the collection of observations that could be produced by a particular data-generating process (DGP).

For example:

  • A survey process might generate responses from all eligible voters.

  • A manufacturing process might generate products coming off an assembly line.

  • A biological process might generate measurements from organisms in a study.

From this perspective, the population represents the broader set of outcomes that the data-generating process could produce.

Why Populations Matter

Defining the population helps researchers:

  • Clarify the question they are trying to answer

  • Decide how to collect data

  • Interpret results appropriately

  • Understand who or what conclusions apply to

A well-defined population is an important part of any statistical investigation.

Challenges

Researchers rarely observe an entire population because populations can be:

  • Very large

  • Constantly changing

  • Difficult to access

  • Expensive to measure completely

As a result, sampling is often necessary.

Example

Suppose a researcher wants to estimate the average number of hours high school students sleep each night.

  • Population: All high school students of interest

  • Sample: The students who are actually surveyed

The sample provides evidence about the population, but it is not the population itself.


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