049. The Mean of the Sample Means

The sampling distribution for the sample means is merely a listing of all possible sample means. These sample means have a mean; it is called the “mean of all possible sample means”, or the Grand mean. The grand mean will always equal the population mean, i. e. = μ. It is calculated in the usual fashion: the individual observations (sample means) are summed, and the result is divided by the number of observations (samples).

, (5.1)

Where N is the population size; N is the number of observations in a single sample; K is the number of possible samples.

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