Random Sample
A random sample is a subset chosen from a population in which every member of that population has a known, often equal, chance of being selected. This method helps ensure the sample fairly represents the whole group.
A random sample is a sample drawn from a population using a probabilistic selection mechanism such that each member's probability of inclusion is known and greater than zero. When every possible sample of a given size is equally likely to be chosen, the result is called a simple random sample (SRS). Random sampling is the foundation of statistical inference because it allows researchers to quantify sampling variability and generalize findings from the sample to the population.
Example
Problem: A school has 800 students. You want to survey a random sample of 50 students about lunch preferences. Describe how to select a simple random sample and determine the probability that any individual student is chosen.
Step 1: Assign each of the 800 students a unique number from 1 to 800. This is your sampling frame — a complete list of the population.
Step 2: Use a random number generator (or a table of random digits) to produce 50 distinct numbers between 1 and 800. Each number corresponds to one student.
Step 3: The students whose numbers were selected form your random sample. Because every student had the same chance of being picked, calculate that probability.
Step 4: Each student has a 6.25% chance of being included. Since every possible group of 50 students was equally likely, this is a simple random sample.
Answer: Each student has a probability of 0.0625 (6.25%) of being selected. The 50 students identified by the random number generator constitute a simple random sample.
Why It Matters
Random sampling is what allows you to draw trustworthy conclusions about a large group without surveying everyone. Opinion polls, medical trials, and quality-control checks all depend on it. Without randomness in selection, results can be biased — meaning they systematically favor certain outcomes — and no amount of sophisticated analysis can fully fix that problem.
Common Mistakes
Mistake: Confusing a random sample with a haphazard or convenience sample
Correction: Picking people who happen to be nearby or who volunteer is not random, even if it feels unplanned. A true random sample requires a defined process where every population member has a known probability of selection.
Mistake: Assuming 'random' means every member must have an equal chance
Correction: In a simple random sample, probabilities are equal. But other valid random sampling methods (like stratified or cluster sampling) can give different members different — but still known — probabilities of selection.