# Sampling Distribution: Definition, Models & Example

Instructor: Tara Lehan

With a doctorate in marriage and family therapy and a certificate in measurement and statistics, Tara has taught social science courses to students of all levels.

Researchers frequently use sample data to draw conclusions about a population using sampling distributions. In this lesson, you will learn about the definition of a sampling distribution and review an example with an illustration.

## Sample and Population

Before we can really explain sampling distribution, we need to do some work with more basic concepts of statistics, which are used by researchers to learn about populations of human beings.

In the context of research, a population refers to all of the units or cases of interest in a study, whereas a sample is a subset of that population from which information is collected. Samples are often used in research because it is not possible or desirable to collect information from every unit or case in a population. For example, suppose that you are interested in learning how long it takes the average adult in your city to travel to work on a typical day. It would likely be too costly and time-consuming for you to collect that information from every adult resident in your city. Instead, you might ask 100 randomly selected adults in your city to provide you with this information and use it to determine their average commute time. That average would be specific to that sample. If you asked another 100 randomly selected adult residents how long it takes them to travel to work on a typical day and calculated their average response, it would likely be slightly different than that of the first sample.

## Statistic and Parameter

Now that you understand the relationship between a sample and a population, let's talk about the association between a statistic and a parameter. A statistic is a value of an attribute for a sample. As described above, researchers often use statistics to estimate the value of a characteristic of a population. This value is called a parameter. That is, statistics are numbers that summarize information from a sample, and parameters are numbers that summarize information for the larger population from which the sample was drawn. A good way to remember the difference is to look at the first letters of the words: a statistic measures some aspect of a sample, and a parameter measures some aspect of a population.

Although researchers use statistics for a variety of reasons, one of the primary purposes is to draw conclusions about the characteristics of a population based on information obtained from a sample. Examples of statistics that are commonly presented in research are the sample mean and standard deviation. These two values are often presented together. The mean refers to the average value. The standard deviation refers to how spread out the values are.

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