The Central Limit Theorem (CLT) states that regardless of the underlying distribution of a dataset, the sampling distribution of the sample means will approximate a normal Distributions as the sample size becomes large.
Key Points
- Mean of Sampling Distribution: The mean of the sampling distribution is equal to the mean of the original population.
- Variance of Sampling Distribution: The variance of the sampling distribution is the population variance divided by the sample size ((n)), making it (n) times smaller.
- Applicability: The CLT applies when calculating the sum or average of many variables, such as the sum of rolled numbers when rolling dice.
Importance
- The CLT allows us to assume normality for various variables, which is crucial for:
- Confidence intervals
- Hypothesis testing
- Regression analysis