Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. This data is normally seen as “numbers.” In applying statistics to a specific problem, it is necessary to begin with a population or process to be studied. Populations can be diverse topics such as “all high school graduates living in a state” or “every highway in a specific state.” It deals with all aspects of data including the planning of data collection and experiments.
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics. Some people consider statistics to be a distinct mathematical science rather than a branch of mathematics. Most colleges list statistics as a mathematics course.
Mathematical statistics is the application of math to statistics. The term statistics was originally conceived as the science of the state. This included the collection and analysis of facts about a country including its economy, land, military, population, etc. Common techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.