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# Sampling Distribution

The sampling distribution is a theoretical concept which describes the range of values from which a statistic is likely to be found and the frequency of selecting a particular value. Commonly, sampling distributions are used in statistics to compute the mean value of a sample. After repeatedly taking samples from a data set, the statistical mean for the sample set can be derived and this statistic will describe the sampling distribution of the mean.

Sampling distributions also assist in explaining the variability associated with a data set.  By understanding the amount of variability which a data set possesses, the likelihood of selecting a particular value can be estimated. Values which are more likely to be selected will lie closer to the mean of the sampling distribution, rather than farther away. Furthermore, the variability of a sample can be estimated by the shape of the distribution when graphed.

Sampling distributions are mainly theoretical in nature because it is not always a practical measure to calculate. In order to conduct this calculation, all possible combinations of samples which can be obtained from a population must be selected (1). With large populations, this is not likely plausible.

Understanding the sampling distribution of a data set is also important for the practice of statistical inference. For example, if you have a population of a particular size, such as n=20, you could calculate the mean or variability of the sampling distribution by estimating the likelihood of obtaining a particular value. The commonality and rareness of selecting values are important when formulating generalizations around a data set. Overall, sampling distributions are critical in analyzing a sample and using statistics to describe their distribution.

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