The range of the sampling distribution of the means is 12 - 4 = 8. In the example that follows, the range of the parent population is 13 - 3 = 10. Since the standard deviation measures the spread of the distribution, and the sampling distribution is always packed tighter around the sampling mean, r x-bar < r. This is because the range of the sample means data is smaller than the range of the population sampled. The standard deviation of a sampling distribution of the means (called sigma x bar) is always less than the standard deviation of the parent population. The mean of a sampling distribution of the means (called mu x bar) is always equal to the mean of the parent population. The Mean & Standard Deviation of the Sampling Distribution of the Means (an option is to list the frequency of each mean: see part 3 of Practice question) To display this distribution, we list the value of each sample mean x-bar and ![]() The Sampling Distribution of the Sample MeansÄefinition: The probability distribution of the sample meansÄerived from all possible samples of a given size from a given population. We then use this new distribution, The Sampling Distribution of the Sample Means, to find the mean of and an estimate for the standard deviation of the parent population. ![]() When we need information about the parameters of a population (especially a finite population) we collect many samples of a given size n from the population, then set up the probability distribution for the means of all our samples. Sampling distr of mu The Sampling Distribution of the Means
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