Law of large numbers

Definition

The Law of Large Numbers states that as the sample size increases, the sample mean will get closer to the population mean. This principle is fundamental in probability and statistics.

5 Must Know Facts For Your Next Test

1. The Law of Large Numbers applies only when samples are independent and identically distributed (i.i.d).
2. There are two forms: Weak Law of Large Numbers and Strong Law of Large Numbers.
3. This law helps justify the use of sample data to make inferences about a population.
4. In practical applications, larger sample sizes typically yield more accurate estimates.
5. The Central Limit Theorem relies on the principles outlined by the Law of Large Numbers.

Review Questions

• What conditions must be met for the Law of Large Numbers to apply?
• How does the Law of Large Numbers relate to the Central Limit Theorem?
• Explain the difference between the Weak and Strong forms of the Law of Large Numbers.

Related terms

Central Limit Theorem:

States that, given a sufficiently large sample size from a population with a finite level of variance, the sample means will be approximately normally distributed.

Sample Mean: The average value calculated from a set of data points collected from a sample.

Population Mean:

The average value calculated from every possible data point in an entire population.