Data that are not sampled from a finite population

There is no real finite population underlying most data sets from which the values can be treated as being sampled. The randomness in such data must be explained in a different way.

Sampling from an abstract population

"Random sampling from a population" is also used to explain variability even when there is no real finite population from which the data were sampled.

We imagine an abstract population of all values that might have been obtained if the data collection had been repeated. We can then treat the observed data as a random sample from this abstract population.

Defining such an underlying population therefore not only explains sample-to-sample variability but also gives us a focus for generalising from our specific data.