What is the sampling distribution?

What is the sampling distribution?

• A. The probability distribution of a statistic.
• B. The distribution of observed data in a single sample.
• C. The distribution of the population.
• D. The distribution of sampling errors only.

Answer: (A)

The sampling distribution is the probability distribution of a statistic. When you repeatedly draw samples of a fixed size from a population and compute a statistic for each sample (for example, the sample mean or sample proportion), the collection of those statistic values across all possible samples forms the sampling distribution. This tells you how the statistic would vary from one sample to another and underpins ideas like standard error and confidence intervals. It isn’t the distribution of the data in a single sample, nor the distribution of the population. It also isn’t just the distribution of sampling errors—the errors are the differences between the statistic and the population parameter, and the sampling distribution describes all possible values the statistic can take across many samples.

The sampling distribution is the probability distribution of a statistic. When you repeatedly draw samples of a fixed size from a population and compute a statistic for each sample (for example, the sample mean or sample proportion), the collection of those statistic values across all possible samples forms the sampling distribution. This tells you how the statistic would vary from one sample to another and underpins ideas like standard error and confidence intervals. It isn’t the distribution of the data in a single sample, nor the distribution of the population. It also isn’t just the distribution of sampling errors—the errors are the differences between the statistic and the population parameter, and the sampling distribution describes all possible values the statistic can take across many samples.