Sampling distribution of a mean

Math

Definition

The probability distribution of all possible sample means from samples of a fixed size drawn from a population. By the Central Limit Theorem, this distribution is approximately normal for large sample sizes, centered at the population mean with standard deviation σ/√n.

Examples

  • Taking many random samples of 30 students' test scores and plotting the average of each sample
  • Measuring the mean weight of 50 apples repeatedly from a large orchard to see how the average varies
Key Fact

Standard error = σ / √n

Related Terms

Central limit theorem Standard deviation Normal distribution Sampling methods

Study This Concept

Practice sampling distribution of a mean with free review games in these units:

AP Statistics Unit 5: Sampling Distributions