Population (Statistics)
In statistics, a population is the complete set of all individuals or items that a study aims to describe.
Definition
A population is the entire group of people, animals, or things you want to learn about in a study, the complete collection of individuals or measurements about which conclusions are desired. Formally, a population is the set of all possible realizations of a random variable $X$ with distribution $F(x; \theta)$, characterized by unknown parameters $\theta$ belonging to a parameter space. Because studying a full population is often impractical, researchers study samples instead, using inference to estimate $\theta$ or test hypotheses about it.
Example
If a researcher wants to know the average height of all 7th graders in the United States, the population is every 7th grader in the country; likewise, a company wanting the average satisfaction rating of all $50{,}000$ of its customers treats those customers as its population, and since surveying all $50{,}000$ is too costly, a sample is taken instead. If heights are normally distributed across a population with mean $\mu$ and variance $\sigma^2$, both $\mu$ and $\sigma^2$ are population parameters, and a sample of size $n$ yields estimates $\bar{x}$ and $s^2$ that converge to these parameters as $n$ grows, by the law of large numbers and consistency of sample variance.
Key Insight
Populations can be huge (all people on Earth) or small (the $30$ students in your class); what makes it a population is that it is the complete group you care about, described by parameters that are usually unknown and estimated from sample statistics. The distinction between population distribution and sampling distribution is fundamental: the sampling distribution of $\bar{x}$ has mean $\mu$ and standard error $\sigma/\sqrt{n}$, shrinking as sample size grows.