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Last month, Polly Yurathane stumbled her way through an explanation of the central limit theorem to her boss, Emily Dickinson. Now that Emily understands that principle, she asks Polly to critique her own simplified view of the theorem. Going to a white board, she begins, “If you take many samples of the size n from any population, calculate the means of each sample, then plot those means as a histogram, three things will happen.” Going on, she lists these:
- The mean of the distribution of sample means will be equal to the mean of the population.
- The shape of the distribution of sample means will be normal.
- The variability of that distribution will be equal to the standard deviation ( ) of the population, divided by the square root of the sample size used to create the distribution of sample means.
Emily had consulted with Dr. Stan Deviation, who emphasizes that the theorem is true regardless of the shape of the population that is being sampled from.
She turns to Polly for verification that her explanation was clear and accurate. Polly has been listening, actually learning for herself the meaning of the central limit theorem. Feeling that she must add something to the explanation, however, she says that the theorem works only when the sample has been taken from a population with a normal distribution, suggesting further that Emily’s understanding would be better enhanced by conversation with herself than by consultation with Dr. Deviation.
Is Polly’s additional observation helpful and accurate?
2007 PQ Systems.
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