The Central Limit Theorem (CLT) is a fundamental concept in statistics that plays a crucial role in the field of probability and inferential statistics. It states that, regardless of the shape of the original distribution, the sampling distribution of the sample mean will tend to be approximately normally distributed for sufficiently large sample sizes.
Here are key points about the Central Limit Theorem:
1. Normal Distribution of Sample Means:
- The Central Limit Theorem asserts that if you repeatedly draw random samples from any population, the distribution of sample means will be normal (or approximately normal) as long as the sample size is sufficiently large, typically
n ≥ 30. This holds true regardless of the shape of the population distribution.
2. Sampling Distribution:
- The sampling distribution is a distribution of a statistic (such as the mean) based on multiple samples drawn from the same population. For example, if you were to calculate the mean of many different samples from a population, the distribution of those means would follow a normal distribution, according to the CLT.
