One implication of the central limit theorem is that a distribution of means will be less variable than a distribution of scores taken from the same population.

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The central limit theorem states that as sample size increases, the distribution of sample means becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. This means that the distribution of means will have less variability than the distribution of scores taken from the same population, which can have a wide range of values.

One Implication of the Central Limit Theorem Is That a Distribution