## Applied Mathematics## Statistics |

## How does one sample a population? |

Sampling is the term used when one obtains a sample of a population; the number of members in the sample is called the *sample size.* As with most mathematical concepts, there are several types of sampling.

*Random sampling* is a technique involving a group of subjects (the sample) from a larger group (population); it is a method that reduces the likelihood of bias. In random sampling, each individual is chosen by chance, with each member of the population having a known (but often unequal) chance of being included in the sample.

*Simple random sampling* also involves a group of subjects (the sample) from a larger group (population), but in this case, each individual is chosen entirely by chance, with each member of the population having an equal chance of being included in the sample. In fact, each member of the population has an equal chance of being chosen at any stage of the sampling process.

*Independent sampling* comprises samples collected from the same (or different) populations that have no effect on one another. In other words, there is no correlation between the samples.

*Stratified sampling* includes random samples from various subgroups (also called subpopulation or stratum of the population) chosen to be representative of the whole population. It is often thought of as a better technique than simple random sampling. For example, if a sheep farmer wanted to determine the average weight (amount) of wool gathered from three types of sheep on his farm, he could divide his flock into the three subgroups and take samples from those groups.

In *cluster sampling* the entire population is divided into clusters (groups); then a random sampling is taken of the clusters. This technique is used when a complete list of the population’s members can’t be studied, but a list of population clusters can be gathered.