State the main points of the Central Limit Theorem for a mean.
http://www.isixsigma.com/dictionary/Central_Limit_Theorem-177.htm
The Central Limit Theorem (CLT) is a fundamental concept in statistics that is used to make inferences about population means. It states the following main points:
1. Large Sample Size: The CLT applies to independent and identically distributed random variables from any population, as long as the sample size is sufficiently large (typically n ≥ 30).
2. Sampling Distribution: When repeatedly sampling from a population and calculating the mean of each sample, the distribution of these sample means will become approximately normally distributed, regardless of the shape of the population distribution.
3. Normality: As the sample size increases, the sampling distribution of the mean becomes increasingly closer to a normal distribution. This means that the mean of the sample means will be approximately equal to the population mean.
4. Mean and Variance: The mean of the sampling distribution of the sample means will be equal to the population mean. The standard deviation (or variance) of the sampling distribution, often referred to as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (σ/√n).
Overall, the Central Limit Theorem allows us to use the normal distribution to make inferences about population means based on sample means, even if the underlying population distribution is non-normal.