What Is a Population Parameter?

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In statistics, a population parameter is a number that describes something about an entire group or population. This should not be confused with parameters in other types of math, which refer to values that are held constant for a given mathematical function. Note also that a population parameter is not a statistic, which is data that refers to a sample, or subset, of a given population. With a well-designed study, you may be able to obtain a statistic that accurately estimates the true value of a population.

Key Takeaways: Population Parameter

  • In statistics, a population refers to all the members of a group of people or things. A population can be large or small depending on what you are interested in studying.
  • A parameter is data that describes the entire population, while a statistic is data that describes a sample of that population.
  • A sample is a part, or a subset, of a population.
  • With a well-designed study, a sample statistic may provide an accurate estimate of a population parameter.

What Is a Population?

In statistics, a population refers to all the members of a group. A population can be large or small depending on what you are interested in studying. For example, a population could be “all the residents of Germany”—which in 2017 was estimated to be about 83 million people—or “all the freshman in a certain high school”—which can range from a single person to a couple thousand depending on the school.

And though you may have heard the term “population” in reference to people, a population can refer to other groups of things as well. For example, you may be interested in studying the population of birds that live near a certain beachside area, or the balloons produced by a specific manufacturer.

Population vs. Sample

No matter how large or small a population may be, a sample refers to a subset, or part, of that population. For example, if the number of freshmen in a high school class is 100, you may choose to study only 45 of the students.

Statistical studies typically use samples instead of populations because it may be costly, time-consuming, or simply impossible to find or reach out to everyone in a population. Nevertheless, if you are conducting a statistical study, you should try to design your study so that it accurately represents the population. For example, if you want a sample representing all the people residing in Germany, you may want to randomly select people from every part of the country.

You should also make sure your sample size, or number of things you are studying, is large enough so that your data becomes statistically significant: it accurately estimates the true statistics regarding a population.

What Is a Parameter?

You may have already heard of parameters in math, which are values that are held constant for a given mathematical function. In statistics, the definition of parameter is different. A parameter is data that refers to something about an entire population. If your population is all the lunches that the students in X high school eat on a certain day, a population parameter might be that 35 percent of the lunches are brought from home.

Parameter vs. Statistic

Parameters and statistics are very similar in that they both say something about a group—for example, that “20% of M&Ms are the color red”—but the key difference is who or what they are describing. Whereas parameters refer to an entire population, statistics refer to part of that population, or the sample of the population that was researched in a study.

For example, in the above example, instead of going through all the M&Ms in existence and counting how many red ones there are to obtain a population parameter, you may count how many red M&Ms are in several packs to obtain your sample’s statistic. If your study was designed well, the statistic you obtain should closely estimate the actual population parameter.