Statistics concerns what can be learned from data. Applied statistics comprises a body of methods for data collection and analysis across the whole range of science, and in areas such as engineering, medicine, business, and law — wherever variable data must be summarized, or used to test or confirm theories, or to inform decisions. Theoretical statistics underpins this by providing a framework for understanding the properties and scope of methods used in applications.

Statistical ideas may be expressed most precisely and economically in mathematical terms, but contact with data and with scientific reasoning has given statistics a distinctive outlook. Whereas mathematics is often judged by its elegance and generality, many statistical developments arise as a result of concrete questions posed by investigators and data that they hope will provide answers, and elegant and general solutions are not always available. The huge variety of such problems makes it hard to develop a single over-arching theory, but nevertheless common strands appear. Uniting them is the idea of a statistical model.