StATS: What is a random sample?
A random sample is one where the researcher insures (usually through the use of random numbers applied to a list of the entire population) that each member of that population has an equal probability of being selected. Random samples are an important foundation of Statistics. Almost all of the mathematical theory upon which Statistics are based rely on assumptions which are consistent with a random sample.
Purely random samples are hard to achieve in the real world, but many times you can come close. The biggest problem is that you may not have a complete list of the population that you want to randomly draw from. The telephone book for a city, for example, will list most households, but will exclude those who do not have a telephone, those who have unlisted numbers, and most recently, those who use a cell phone instead of a land phone for all their calls (cell phone numbers are usually not in the telephone book).
A second barrier to purely random samples is that for some people in the population, you will find it difficult or impossible to locate them. People who work unusual hours or who travel a lot may end up getting selected in the sample, but may never be around to answer the telephone.
Further reading
This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Research designs.