In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability.
[2] The principle of simple random sampling is that every set with the same number of items has the same probability of being chosen.
Sampling done without replacement is no longer independent, but still satisfies exchangeability, hence most results of mathematical statistics still hold.
It requires a complete sampling frame, which may not be available or feasible to construct for large populations.
Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.
Advantages are that it is free of classification error, and it requires minimum previous knowledge of the population other than the frame.
Its simplicity also makes it relatively easy to interpret data collected in this manner.
For these reasons, simple random sampling best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity.
An example would be if the students in the school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 0533, and then picked every 10th name thereafter to give us our sample of 100 (starting over with 0003 after reaching 0993).
In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the remainder.
If the members of the population come in three kinds, say "blue", "red" and "black", the number of red elements in a sample of given size will vary by sample and hence is a random variable whose distribution can be studied.
That distribution depends on the numbers of red and black elements in the full population.
For a simple random sample without replacement, one obtains a hypergeometric distribution.
[10] The algorithm simply assigns a random number drawn from uniform distribution