Sampling distribution

A sampling distribution is the probability distribution of a statistic across repeated samples drawn under the same conditions. It describes how the statistic varies because of sampling.

Central limit theorem: A theorem describing conditions under which standardized sums or sample means approach a normal distribution. It explains why many sample-mean distributions become approximately normal as sample size grows.
Statistic: A function of sample data that summarizes information or supports inference about a population. A sampling distribution is defined for a chosen statistic, such as a mean or proportion.
Confidence interval: A range of parameter values produced by a procedure with a specified long-run coverage rate. Confidence intervals use sampling distributions to quantify the uncertainty of an estimate.
Probability distribution: A mathematical description assigning probabilities to the possible values of a random variable. A sampling distribution is this general object applied specifically to a statistic across samples.
Standard error: The standard deviation of a statistic's sampling distribution. It measures the spread of this distribution and typically shrinks as sample size increases.
Parameter (statistics): A fixed numerical characteristic of a population, such as its mean or variance. Unlike a statistic, a parameter stays fixed while the statistic varies across samples.
Hypothesis test: A procedure that uses sample data to evaluate a claim about a population. A test compares an observed statistic with its distribution under the null hypothesis.
Empirical distribution function: The step function giving the fraction of observed data at or below each value. It describes observed data values, not the variation of a statistic across hypothetical samples.
Sample mean: The arithmetic average of observations in a sample. Its sampling distribution is a central example, with behavior governed by population variance and sample size.
Random variable: A variable whose possible values are associated with probabilities. Before data are observed, a statistic computed from a random sample is itself a random variable.

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