Which statement best describes the concept of a sampling distribution?

• A. The distribution of observed data values in a single sample.
• B. The distribution of a statistic across all possible samples.
• C. The probability distribution of a statistic across all possible samples of a fixed size drawn from the population.
• D. The distribution of p-values across repeated studies.

Answer: (C)

A sampling distribution is about how a statistic (like a mean or proportion) would vary if you could take many samples from the population. It’s the probability distribution that tells you how likely each possible value of that statistic is, across all possible samples of a fixed size drawn from the population. That idea captures the randomness coming from sampling itself, not just what one particular sample looks like.

This is why the statement describing the probability distribution of a statistic across all possible samples of a fixed size from the population is the best description. It emphasizes both the repeated-sampling nature and the distribution of the statistic, not the data from just one sample.

For context, think of taking lots of samples of 30 people and computing the average height for each sample. Those many sample means won’t all be the same; they cluster around the true population mean, with a spread determined by the sample size and population variability. That clustering is the sampling distribution of the sample mean.

The other options don’t fit as well. The distribution of observed data values in a single sample describes only one dataset, not how a statistic would vary across samples. A statement about the distribution of a statistic across all possible samples is close but misses the explicit emphasis on the probability distribution for fixed-size samples drawn from the population. The distribution of p-values across repeated studies concerns inferential outcomes, not the sampling distribution of a statistic itself.