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What Is The Central Limit Theorem-ECO6416

What Is The Central Limit Theorem-ECO6416 - What Is The...

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What Is The Central Limit Theorem? The central limit theorem (CLT) is a "limit" that is "central" to statistical practice. For practical purposes, the main idea of the CLT is that the average (center of data) of a sample of observations drawn from some population is approximately distributed as a normal distribution if certain conditions are met. In theoretical statistics there are several versions of the central limit theorem depending on how these conditions are specified. These are concerned with the types of conditions made about the distribution of the parent population (population from which the sample is drawn) and the actual sampling procedure. One of the simplest versions of the central limit theorem stated by many textbooks is: if we take a random sample of size (n) from the entire population, then, the sample mean which is a random variable defined by: Σ x i / n, has a histogram which converges to a normal distribution shape if n is large enough. Equivalently, the sample mean distribution approaches to normal distribution as the sample size increases. Some students having difficulty reconciling their own understanding of the central limit theorem with some of the textbooks statements. Some textbooks do not emphasize the on the

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