Sampling Distribution vs Population

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.

A population includes every member of the group in question, not just the ones you happen to observe. For example, if you want the average height of all students at a school, the population is all of those students, and its true mean height is a fixed number you usually cannot measure directly. A numerical fact about a population, such as the population mean (the Greek letter mu, written $\mu$), is called a parameter. You typically estimate it from a smaller sample.