Sampling Distribution (1 of 3)

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If you compute the mean of a sample of 10 numbers, the value you obtain will not equal the population mean exactly; by chance it will be a little bit higher or a little bit lower. If you sampled sets of 10 numbers over and over again (computing the mean for each set), you would find that some sample means come much closer to the population mean than others. Some would be higher than the population mean and some would be lower. Imagine sampling 10 numbers and computing the mean over and over again, say about 1,000 times, and then constructing a relative frequency distribution of those 1,000 means. This distribution of means is a very good approximation to the sampling distribution of the mean. The sampling distribution of the mean is a theoretical distribution that is approached as the number of samples in the relative frequency distribution increases. With 1,000 samples, the relative frequency distribution is quite close; with 10,000 it is even closer. As the number of samples approaches infinity, the relative frequency distribution approaches the sampling distribution.