Sampling Distribution of the Mean

The mean is the most widely used measure in statistics. In Section 4.1, you learned that the mean is calculated by summing the observed numerical values, then dividing the sum by the number of values:

Because the mean is based on the computation of all the values in the sample, it can vary from sample to sample, especially when extreme values, or outliers, are present. Statisticians developed the Central Limit Theorem to describe the behavior of the sampling distribution of the mean.

Central Limit Theorem

Regardless of the shape of the distribution of the individual values in a population (frame), as the ...

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