Population and census

We often want to find information about a particular group of individuals (people, fields, trees, bottles of beer or some other collection of items). This target group is called the population.

Collecting measurements from every item in the population is called a census. A census is rarely feasible, because of the cost and time involved.

Simple random sample

We can usually obtain sufficiently accurate information by only collecting information from a selection of units from the population — a sample. Although a sample gives less accurate information than a census, the savings in cost and time often outweigh this.

The simplest way to select a representative sample is a simple random sample. In it, each unit has the same chance of being selected and some random mechanism is used to determine whether any particular unit is included in the sample.

Sampling from a population of values

It is convenient to define the population and sample to be sets of values (rather than people or other items). This abstraction — a population of values and a corresponding sample of values — can be applied to a wide range of applications.