Cluster and systematic sampling are practical alternatives when a simple random sample is too costly or awkward.
Both trade some statistical precision for a large saving in time or money.
They suit fieldwork, audits and production lines, where members are found in groups or in sequence.
In cluster sampling the population is split into natural groups, and a random set of whole groups is chosen.
For example, surveying every pupil in 20 randomly chosen schools avoids travelling to hundreds of schools.
Members of one cluster are often alike, such as pupils from one area, so each extra pupil adds less new information.
That makes cluster samples less precise than simple random samples of the same size.
In 2-stage cluster sampling, clusters are chosen at random and then members are sampled within each one.
In systematic sampling the gap k is the population size divided by the sample size, so 10,000 invoices and a sample of 200 give 50.
A random start between 1 and k keeps every member's chance of selection equal.
The method spreads the sample evenly through the list, which is convenient on a production line or in a ledger.
A list sorted by something relevant, such as invoice value, makes a systematic sample cover the full range.
A repeating pattern in the list that matches the gap ruins the method, such as a 7 day gap in daily data.
In practice, both methods are common in audits, quality checks and national surveys.
The usual mistake is analysing a cluster sample as if it were a simple random sample, which overstates its precision.