Even if individual scores aren’t normally distributed, though, researchers tend to make statistical inferences about summaries of scores, like measures of central tendencies, and the distribution of those values will tend to be normal regardless of the distribution of individual scores. When we deal with big sample sizes (more than 30), and we take repeated samples from a population, the means of those samples will distribute themselves pretty closely to the shape of a normal curve. This is very important, because a lot of what we do when we talk about inferring from a sample to a population
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