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Statistics and Probability
Finding the Mean and Variance of the Sampling Distribution of Sample Means | With Replacement

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

The variance of the sampling distribution of the mean is computed as follows: That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean).

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