Sample Mean (xbar) (from Internet Glossary of Statistical Terms)

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Sample Mean ()
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The statistic is a measure on a sample that is used an an estimate of the mean (Mu x) of the population from which it was drawn. Regardless of the size of the population and regardless of the size of the random sample, it can be shown (through The Central Limit Theorem) that if we repeatedly took random samples of the same size from the same population, the sample means would cluster around the exact value of the population mean. Another way to say this is to assert that is an unbiased estimate of Mu x.

As illustrated here, our random sample contains 4 items and it was drawn from a population that contains 9 items. Most statisticians use (n) to represent the number of items in a sample, whereas they use the symbol (N) to represent the number of items in a population. For this sample from this population n=4, N=9.

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