According to the principle of probability, what does the law of large numbers state?

The law of large numbers is a fundamental principle in probability and statistics that states that as the size of a sample increases, the sample mean will converge towards the population mean (the true average of the entire population). This concept is crucial because it provides the foundation for making inferences about populations based on sample data.

When a random sample is taken from a population, individual variations can cause the sample mean to differ from the population mean. However, as more and more observations are included in the sample—meaning the sample size grows—the influence of those individual variations diminishes. Consequently, the sample mean becomes a more accurate estimate of the population mean.

This principle reinforces the importance of using larger sample sizes in statistical research and sampling methods, as larger samples will yield more reliable results that are representative of the population from which they are drawn.