Definition
A random sample is a subset of a population selected by a procedure that gives every member of the population a known, non-zero probability of inclusion. In the simplest case — simple random sampling — every member has an equal probability and every possible subset of the chosen size is equally likely. More elaborate schemes (stratified, cluster, systematic) preserve the random-selection property while constraining how the draws are organised.
The defining feature is procedural, not aesthetic. A sample is "random" because of how it was selected, not because the resulting list looks scattered. A handful of "random" passers-by interviewed at one street corner is not a random sample of any defined population — it is a convenience sample, and its statistical properties are unknowable.
Why it matters
How it works
A simple random sample requires two ingredients: a sampling frame — a list of every member of the target population — and a randomisation mechanism, traditionally a random-number table and today a software pseudo-random generator. Each draw is independent of the others and gives every remaining member the same chance of being picked. The result is that any statistic computed from the sample — a mean, a proportion, a standard deviation — has a known sampling distribution: the spread of values that statistic would take across many hypothetical samples drawn the same way. That known distribution is what lets analysts attach a margin of error or a confidence interval to a single estimate.
When the sampling frame is imperfect, the randomness alone does not save the design. Undercoverage — when some part of the target population is missing from the frame — produces bias that does not shrink as the sample grows. The 1936 Literary Digest poll drew over 2 million ballots from car-owner and phone-subscriber lists, predicted a Landon victory, and got the result spectacularly wrong: the frame systematically excluded the poorer voters who turned out for Roosevelt. Non-response compounds the same problem when invited respondents disproportionately refuse. The practical defence is twofold: design the frame to cover the target population as completely as possible, and follow up vigorously to convert non-respondents, since a 60% response rate on a well-designed frame beats a 30% response rate on a larger one.