## What is the sampling distribution for a statistic?

## Answer

When you collect multiple samples from the same population, you will get a variety of sample statistics. If you survey two different groups of women about their age, you will most likely not get the same mean age for each sample.

You can use a sampling distribution to describe the distribution of the statistic if a large number of samples were taken. In other words, the statistic is a random variable with its own probability distribution. For example, the sampling distribution of the sample mean \(\bar{x}\) can be written as \(\bar{x} \sim N(\mu, \sigma^2/n)\), where \(\mu\) is the population mean, \(\sigma^2\) is the population variance, and n is the sample size. Having knowledge about the sampling distribution is very useful when performing statistical inference.