Population (statistics) in the context of Statistical sample

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population (in many cases, collecting the whole population is impossible, like getting sizes of all stars in the universe), and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications.

Survey methodology is "the study of survey methods".As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving the number and accuracy of responses to surveys. Survey methodology targets instruments or procedures that ask one or more questions that may or may not be answered.

Researchers carry out statistical surveys with a view towards making statistical inferences about the population being studied; such inferences depend strongly on the survey questions used. Polls about public opinion, public-health surveys, market-research surveys, government surveys and censuses all exemplify quantitative research that uses survey methodology to answer questions about a population. Although censuses do not include a "sample", they do include other aspects of survey methodology, like questionnaires, interviewers, and non-response follow-up techniques. Surveys provide important information for all kinds of public-information and research fields, such as marketing research, psychology, health-care provision and sociology.

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.

In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently.

Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the long-run probability) as the limit of its relative frequency in infinitely many trials.Probabilities can be found (in principle) by a repeatable objective process, as in repeated sampling from the same population, and are thus ideally devoid of subjectivity. The continued use of frequentist methods in scientific inference, however, has been called into question.

The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation. In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, for example, the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning.

In statistics, the mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmax_xi P(X = x_i). In other words, it is the value that is most likely to be sampled.

Like the statistical mean and median, the mode is a summary statistic about the central tendency of a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, but it may be very different in highly skewed distributions.