What Is a Population in Statistics?
In statistics, a population is the group from which a sample is drawn for a study. Any selection grouped by a common feature can be regarded as a population. A sample is a representation, often statistically significant, of the larger population.
Key Highlights
- In statistics, a population is the entire group on which data is gathered and analyzed.
- Surety in data collection for an entire population is costly and time-consuming; hence, samples are often used for making inferences.
- A random sample must be chosen for results to accurately reflect the population as a whole.
Understanding Populations
Statisticians, scientists, and analysts strive to discern the characteristics of every entity within a population to draw the most accurate conclusions. Although this is often impractical since entire populations usually consist of numerous members. A sample of the population allows analysis despite constraints of time, resources, and access.
Note
In statistics, the term ‘individual’ does not always denote a person. An individual refers to a single entity in the studied group.
Consider the example: Marine biologists cannot realistically gather data on all great white sharks in the ocean (the entire population). They tag a sample of easily reachable sharks and gather data from this group to infer characteristics of the whole population. This approach typically adheres to random sampling since encounters with great whites are to a degree random. A valid statistic can emerge from a sample or an entire population. The goal of random sampling is eliminating bias in the results—a sample must give every member of the whole population an equal chance of selection.
Measuring a Population
The challenge of measuring a population varies with the objective. Data often get collected via surveys, measurements, observation, or alternate means.
Due to cost, time, and resources required, comprehensive data gathering on a large population is rarely viable. For instance, advertisements claiming, “62% of doctors recommend XYZ” rarely contact every applicable doctor. Rather, from hundreds or thousands surveyed, the percentage stems from the positive responses—a population sample.
Population and Investing
A parameter describes characteristics of a population; a statistic describes characteristics of a sample. Statistics like averages (means) and standard deviations, often derived from population data, are population parameters usually symbolized by Greek letters such as µ (mu) and σ (sigma). More often, inferential statistics predicate their findings on sampled data.
For instance, market and investment analysts scrutinize investment data to draw inferences about the market, specific investments, or indexes. Financial analysts, in some cases, can appraise an entire population given extensive historic price data. Public stock prices represent collective, historical documentation—a complete population in investment terms. Comparatively, stock prices of all tech companies since 2010 could constitute another population.
Here’s an outline of parameters used in different domains:
Investment Analysts
- Alpha: The excess returns of an asset beyond a benchmark.
- Standard Deviation: Average amount of price variability, indicative of risk and volatility.
- Moving Average: Smooths short-term price fluctuations, signaling trends.
- Beta: Measures performance relative to market.
Statisticians and Scientists
- Alpha: Probability of Type I error—rejecting a true null hypothesis.
- Standard Deviation: Variability average in data.
- Moving Average: Reduces short-term data value fluctuations.
- Beta: Probability of Type II error—not rejecting a false null hypothesis.
Essential Questions on Population
What Is the Population Mean?
A population mean is the average value you’re measuring within a given population.
Examples of a Population
- All green-eyed children in the U.S. under age 12.
- All great white sharks in the ocean.
Outstanding Example of a Population
Consider a teacher assessing the standardized test performance of students. The score data of all fifth-graders in the U.S. constitute the reference population.
Conclusion
In statistics, populations are the broad groups from which data extraction occurs. Given the challenge in obtaining comprehensive data, random sampling becomes indispensable. Representative samplings effectively infer characteristics and insights about diverse populations. In investment contexts, populations typically relate to specific asset types or performance metrics, whose recorded historical datasets facilitate more manageable study and insightful analysis.
Related Terms: sample, random sampling, bias, population parameter.
