sampling distribution

A sampling distribution is the probability distribution of a sample statistic, such as the sample mean. In statistics, data is often collected from a sample of a population to make inferences about that population.12

The methods of statistical inference, particularly estimation, rely on probability samples, where each element has a known chance of being included. A simple random sample is a fundamental type, ensuring every possible sample of a given size has an equal chance of selection.2

Knowledge of the sampling distribution is crucial for constructing interval estimates of population parameters. Without a probability sample, the sampling distribution cannot be determined, preventing the creation of such estimates. The central limit theorem is a key concept, stating that the distribution of a sample mean approximates a normal distribution as the sample size increases.234