Sampling Distribution vs Sample

A sampling distribution describes how a statistic, such as the sample mean, changes from one random sample to the next. For example, taking many samples of 40 students and recording each sample mean builds up the sampling distribution of $\bar{x}$ (x-bar, the sample mean). For the sample mean its center is the population mean $\mu$ (mu) and its spread, the standard error, is $\frac{\sigma}{\sqrt{n}}$ (sigma over the square root of n). This spread shrinks as the sample size grows, so larger samples give more consistent estimates.

Because measuring an entire population is often impossible, you gather data from a smaller sample and use it to make estimates. For example, polling 1,000 voters to estimate how all voters will act treats those 1,000 people as the sample. A numerical summary of a sample, such as the sample mean (written $\bar{x}$, read as x-bar), is called a statistic. A well-chosen random sample lets that statistic stand in for the unknown population value.