Review of the Sampling Distribution of the Mean

The sampling distribution of the mean is a theoretical distribution. If you were to draw an infinite number of samples with a particular sample size from a population you would get an infinite number of sample means (one for each sample you drew). The distribution of these means is the sampling distribution of means for your population at that particular sample size.

The shape of the sampling distribution depends on the shape of the population distribution and the size of the sample. Even if the population distribution is not normal, the shape of the sampling distribution of the mean approaches normal as the size of the samples increases. The mean of the sampling distribution is equal to the population mean, and the variance of the sampling distribution is equal to the population variance divided by the sample size. These facts are summarized in the Central Limit Theorem.

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