Simple Random Sample
In short: Simple random sample (SRS) is a selection method in which every possible team of n individuals drawn from the population is exactly as likely to be the one chosen as any other team.
AP StatisticsStatisticsAP Statistics Unit 1
What is Simple Random Sample?
A simple random sample gives every possible team of the chosen size an equal shot, not merely every person. That stronger demand means a set of friends, neighbors or classmates is as likely to land together as any other set.
This differs from a plain “random” selection that gives each person the same chance but forbids some combinations. Picking one name from each homeroom, for example, gives everyone an equal chance yet makes certain groups impossible. An SRS is the baseline design on which most inference formulas are built.
How to spot it
- A study says individuals were chosen by a random number generator, a lottery draw or a table of random digits, as in a simple random sample.
- A formula or conclusion requires that the sample be random and independent.
- The description mentions a complete list of the population, such as a school roster.
- You must explain why a sample is or is not an SRS.
The method
- To draw a simple random sample, get a complete list of the population and label each member with equal-length numbers, such as 01 to 40.
- Generate labels with a calculator’s random integers or with a digit table, reading the digits two at a time.
- Skip labels outside the range and any repeats until you have \(n\) different individuals.
- Record the chosen members; any collection of \(n\) people had the same odds of ending up in your simple random sample.
Simple Random Sample: solved example
Problem
A 40-member debate club is numbered 01 to 40. A teacher reads two-digit pairs from a random digit table: 81 07 33 07 19 40 35 12. Select an SRS of 5 members, and count how many different samples of size 5 were possible.
Solution
Read in order: 81 is above 40, skip it. 07 is chosen; 33 is chosen; 07 repeats, skip it; 19 is chosen; 40 is chosen; 35 is chosen. That gives five members: 07, 33, 19, 40, 35. The pair 12 is not needed.
The number of equally likely samples is \(\binom{40}{5} = 658{,}008\), and each had the same chance \(\frac{1}{658{,}008}\).
Try it
Question 1
A principal picks one random student from each of the 20 homeroom classes. Is this an SRS of 20 students?
Show the answer
No. Everyone has an equal chance, yet two students from one homeroom can never be picked together, so some groups of 20 are impossible.
Question 2
Why is surveying the first 30 people who arrive at a school dance not an SRS?
Show the answer
Early arrivals may differ from late ones, and many groups of 30 (including ones with late arrivals) could never be selected.
Simple Random Sample vs. Stratified Random Sampling
In an SRS, individuals are drawn from the whole population in one pool. In stratified random sampling, the population is first split into groups, and a separate SRS is taken from each one. The second design guarantees every group is represented; the first does not.
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Related words
- Stratified Random Sampling
- Sampling Bias
- Random Sample
- Sampling Distribution
- Population (Statistics)
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