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In the most straightforward case, such as the sentencing of a batch of material from production (acceptance sampling by lots), it is possible to identify and méasure every single item in the population and to include any one of them in our sample. However, in the more general case this is not possible. There is no way to identify all rats in the set of all rats. There is no way to identify every voter at a forthcoming election (in advance of the election).

These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical théory.

As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample. For example, in an electoral poll, possible sampling frames include: