A sampling distribution is the probability distribution for which one of the following: 

Key Points 

• A sampling distribution refers to the probability distribution, under repeated sampling, of a statistic derived from a sample of size n drawn from a particular population. The sample statistic is a measure used to quantify some characteristic of a sample, such as its mean or its variance. 
• Consequently, the shape spread and central tendency of this distribution can provide important insights about the population from which the samples were drawn, including how these characteristics would change under repeated sampling.
• This is a fundamental concept in the fields of statistics and probability, particularly in hypothesis testing and the creation of confidence intervals.

Additional Information

• The concept of a sampling distribution is crucial in inferential statistics, which involves making predictions or inferences about a population based on a sample from that population.
• A key feature is the central limit theorem, which states that if you draw a large number of independent, identically distributed random variables from any population, the distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution.
• Therefore, by studying the sampling distribution of a statistic, we can infer properties about the population and assess the accuracy and reliability of the estimates derived from the sample data.

Hence, a sampling distribution is the probability distribution for sample statistics.