Central Limit Theorems
The Central Limit Theorem (CLT) is a fundamental principle in statistics that states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the original population's distribution. This means that even if the data is skewed or not normally distributed, the averages of sufficiently large samples will tend to form a bell-shaped curve.
The CLT is crucial for making inferences about populations based on sample data. It allows statisticians to use the normal distribution to estimate probabilities and confidence intervals, making it easier to analyze data and draw conclusions in various fields, including economics, psychology, and health sciences.