Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. The evolution of statistics was, in particular, intimately connected with the development of European states following the peace of Westphalia (1648), and with the development of probability theory, which put statistics on a firm theoretical basis.

In early times, the meaning was restricted to information about states, particularly demographics such as population. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, “statistics” means both sets of collected information, as in national accounts and temperature record, and analytical work which requires statistical inference. Statistical activities are often associated with models expressed using probabilities, hence the connection with probability theory. The large requirements of data processing have made statistics a key application of computing. A number of statistical concepts have an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.