Statistical population

A statistical population is the collection of units, outcomes or distributional cases about which an analysis seeks conclusions. A finite population may consist of $N$ fixed values $y_1,\dots ,y_N$, with population mean ${\mu }_N=N^{-1}{\sum }_i{y}_i$. A superpopulation model instead describes observations through a probability distribution.

These viewpoints support different sources of randomness. In sampling from a fixed finite population, selection is random even if each value is fixed. Under simple random sampling without replacement, every unit has inclusion probability $n/N$, and the sample mean is unbiased for ${\mu }_N$. The accessible sampling frame can differ from the target population, producing a coverage problem that a large sample alone cannot repair.