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It is often useful to think of the data as a random sample of the population from which the data were obtained. Random samples consist of an equal number from each category of a population, in a sense that is equivalent to random selection from the population on a probabilistic basis. If a data set is selected as a random sample, individual elements of the data set can be assumed to be drawn "at random" from the larger population.[63][64] Statistical inference is frequently based on requirements of random sampling, such as independence and statistical representativeness for finite samples. Many statistical methods are developed in the context of random sampling design.

Heuristics are informal rules of thumb that are not based on the standard practices of randomized sampling. Heuristics are often used in data mining and data analysis.[65] Heuristics can take the form of table-driven approaches, in which the analysis is simply guided by the presence or absence in the data of certain limits, inequalities, or classes.[66] They are often used as the starting point for formal statistical analysis.[67]

Sampling — an informal term for the use of a random sample — is the gathering of data by selection. The most important distinction between sampling and other forms of data collection is that a random sample is obtained by drawing a single member at random from a larger population or population unit. Most researchers use random samples of data because of the large potential cost of a larger sample.[68] Sampling is a form of finite selection, and therefore the set of samples is always incomplete. The sampling-based design of experiments is a statistical method for deciding the type and number of stores where a new store should be located.

The primary task of probability theory is to determine sets of rules for the conditional distribution of a random variable given the value of a second variable. The general form of a conditional probability is given by: d2c66b5586

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