The Law of Large Numbers and the Central Limit Theorem

Abstract

When pollsters ask a question such as “Do you approve of the job performance of the president?” they usually take large samples. They expect the sample percentage to be close to the population percentage, but they are never certain if their results are accurate. likewise, suppose you toss a coin over and over again and keep track of the percentage of heads obtained along the way. You expect to get heads half of the time, but that doesn’t mean that you’ll get exactly 50 heads in the first 100 tosses. As the number of tosses goes up, you expect the sample percentage to approach 50%, but there will be variability.