Population and Samples

A population is the totality of the observations with which a statistician is concerned. The observations could refer to anything of interest, such as persons, animals or objects; it need not be limited to people. The size of the population is defined to be the number of observations in the population. In collecting data concerning a population, the statistician is often interested in arriving at conclusions involving the entirety of the population.

A sample is a subset of a population. In the process of data gathering, it is often impossible or impractical to obtain the entire set of observations for the given population. Often, a sample of the population is taken, data collected from it, and inferences about the population are made based on the analysis of the sample data.

Data collected from a sample that is not representative of the population will often result in inferences that consistently overestimate or underestimate some population characteristic; these are called biased samples. On the contrary, unbiased samples are statistically similar to their parent population, and inferences on a population based on unbiased samples are more reliable than those based on biased samples.

A random sample of n observations is a sample with n observations, selected in such a way that every such sample of the population has the same probability of being selected. These samples are considered to be unbiased. The field of sampling theory deals with the process of selecting random samples, collecting data from these samples, and analyzing it to develop inferences about the population as a whole.