Each sample mean is then treated like a single observation of this new distribution, the sampling distribution. The sampling distribution is a theoretical distribution.

The genius of thinking this way is that it recognizes that when we sample we are creating an observation and that observation must come from some particular distribution. If this is discovered, then we can treat a sample mean just like any other observation and calculate probabilities about what values it might take on.

Central Limit Theorem — Given a random variable with known mean μ and known standard deviation, σ , we are sampling with size n , and we are interested in two new RVs: the sample mean, X - . If the size…. Mean — a number that measures the central tendency; a common name for mean is "average." The term "mean" is a shortened form of "arithmetic mean." By definition, the mean for a sample…. Sampling Distribution — Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability…. genius of thinking this way — that it recognizes that when we sample we are creating an observation and that observation must come from some particular distribution.