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Question 346:



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If a population or sample is not normally distributed (say it is positively skewed) the mean will be affected and not be an accurate representation of the center of the distribution. Positively skewed populations are things like salaries of employees, home values (very large values skew the whole distribution to the right).

The Central limit theorem shows that as sample sizes get larger the sampling distribution of the mean of any type of distribution begins to resemble the normal distribution. This is especially the case as the sample size gets above 30.

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