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Sampling Distribution of the Mean Sampling Distribution The sampling distribution of the mean refers to the probability distribution of means for all possible random samples of a given size from some population. Viewing the variability of all the samples identifies whether one occurrence of the mean is unusual (significant). Mean of all sample means The mean of the sampling distribution of the mean always equals the mean of the population. µx Symbols Type of Distribution Mean Standard Deviation Sample X s Population µ σ Sampling distribution of the mean µx σx Sampling distribution demonstration Central Limit Theorem Regardless of the population shape, the shape of the sampling distribution of the mean approximates a normal curve if the sample size is sufficiently large. Three key characteristics of the sampling distribution of the mean The mean of the sampling distribution equals the population mean 2. The standard error equals the population standard deviation divided by the square root of the sample size 3. The shape of the curve approximates a normal curve 1. Bottom Line Sampling distribution is the most important concept in inferential statistics. The sampling distribution of the mean is defined as the probability distribution of means for all possible random samples of a given size from some population.