According to the Law of Large Numbers, what happens as the sample size increases?

The Law of Large Numbers states that as the number of trials or observations increases, the sample mean will tend to get closer to the expected value or population mean. This phenomenon occurs because larger sample sizes reduce the influence of random variation, providing a more stable and reliable average.

As the sample size increases, the variability of the sample mean decreases, leading to predictions that are more accurate and reflective of the actual population characteristics. This principle is fundamental in statistics as it underpins the rationale for gathering larger samples when conducting surveys or experiments to ensure that the results are representative and trustworthy. The consistent behavior of large samples makes it easier to generalize findings to the broader population, which is why the prediction becomes more accurate with larger sample sizes.