What is a sampling distribution?

• A. The probability distribution of the population parameter.
• B. The probability distribution of a statistic obtained from repeated samples.
• C. The distribution of all possible data values in a population.
• D. The derivative of the likelihood function with respect to a parameter.

Answer: (B)

A sampling distribution describes how a statistic varies when you repeatedly draw random samples from the same population. It is the probability distribution of that statistic across many possible samples. For example, if you take lots of samples of size n and compute the sample mean each time, the collection of those means forms the sampling distribution of the mean. This concept matters because it shows the variability introduced by sampling, not by the population itself—the population parameter is fixed, but the statistic can differ from sample to sample. The sampling distribution helps us understand, for instance, how close our sample mean tends to be to the true mean and how its spread (the standard error) depends on sample size. The other descriptions don’t fit: the population parameter is not a random variable in this framework; the distribution of all possible data values describes the population distribution, not the variability of a statistic from samples; and the derivative of the likelihood is a calculus object, not a probability distribution.