Population: Definition and How to Measure It

Definition

In statistics, a population is the complete set of items, events, or individuals being studied. A sample is a subset of that population selected for measurement or analysis. When researchers cannot measure every member of a population, they use samples to make inferences about the whole.

Key takeaways

• A population is the entire group under study; a sample is a portion of that group.
• Gathering data from an entire population is often impractical because of cost, time, and accessibility.
• Random sampling—where every member has an equal chance of selection—is essential to avoid bias.
• A characteristic measured in a population is a parameter; the same characteristic measured in a sample is a statistic.

Understanding populations and samples

Statisticians and scientists ideally want data for every member of a population, but populations are frequently large or hard to access. Instead they select samples and use inferential statistics to estimate population parameters.

Fast fact: In statistics, an “individual” can be any single entity in the study (a person, a plant, a transaction, an animal, etc.), not necessarily a human.

Example of sampling

Tagging a manageable number of great white sharks and studying them illustrates random sampling. Researchers collect data from the tagged sharks and use those observations to draw conclusions about the broader population of great whites. The accuracy of such inferences depends on how representative the sample is.

How to measure a population

Measuring a population involves collecting data through methods such as surveys, direct measurement, observation, or administrative records. Because measuring every member is often impractical, researchers:

• Define the population clearly (who or what is included).
• Choose an appropriate sampling method (random, stratified, cluster, etc.).
• Collect and analyze sample data to estimate population parameters.
• Assess uncertainty using confidence intervals and hypothesis tests.

Beware of biased claims: for example, an advertisement stating “62% of doctors recommend X” typically reflects the percent among those surveyed—not necessarily the entire population of doctors.

Parameters vs. statistics

• Parameter: a numerical characteristic of a population (e.g., population mean µ, population standard deviation σ).
• Statistic: a numerical characteristic calculated from a sample (e.g., sample mean x̄, sample standard deviation s).

Inferential statistics use sample statistics to estimate population parameters and quantify the uncertainty of those estimates.

Population in investing and finance

Analysts often treat a data set such as decades of recorded prices as a population because historical prices are available for every trading day. In finance, some commonly used measures overlap in name with statistical terms but have context-specific meanings:

Investment analysts
* Alpha: excess return of an asset compared to a benchmark.
* Beta: sensitivity of an asset’s returns to market returns.
* Standard deviation: volatility of price returns.
* Moving average: a smoothing technique to identify trends.

Statisticians/scientists
* Alpha: probability of a Type I error in hypothesis testing.
* Beta: probability of a Type II error in hypothesis testing.
* Standard deviation, moving average: similar mathematical meanings, applied to general data.

Practical note: When complete data for the population are available (e.g., full historical price records), analysts can compute parameters directly and do not need to rely on sampling inference.

Common questions

What is meant by “population” in statistics?
* The entire set of items or events under study (e.g., “all daisies in the U.S.”).

What is the population mean?
* The average of all values of interest across the whole population (denoted µ).

What statistics describe a population?
* Size, density, distribution, mean, variance/standard deviation, and other summary measures.

Conclusion

A population is the full group researchers want to understand; samples provide practical, cost-effective ways to estimate population characteristics. Proper sampling—especially random selection—and clear distinction between parameters and statistics are fundamental to producing reliable, generalizable results.