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Sampling distributions are important since they help us to understand how sample statistics operate and which ones are good estimators of the actual but unknown population parameter.

This Central Limit Theorem Demo deals with the sampling distribution of the mean but it is important to remember that all statistics have a sampling distribution.

The standard deviation of the sample means is called the standard error of the mean. It is found by dividing the population standard deviation by the square root of the sample size.

Remember that sampling distributions are theoretical distributions - constructed under idealized simplifying assumptions. If you actually performed an experiment you would be able to construct a relative frequency table that should approximate the theoretical probability - but for sampling distributions we actually have an infinite number of samples of a fixed size - something that can only be theoretically (and not empirically) determined!