Adiscipline, principally withinapplied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation ofdata.
Statistics is the only mathematical field required for many social sciences.
As forstatistics, the foundations include, on any interpretation of which I have ever heard, the foundations of probability, as controversial a subject as one could name. As in other sciences, controversies over the foundations ofstatistics reflect themselves to some extent in everyday practice, nut not nearly so catastrophically as one might imagine.[…]It is hard to judge, however, to what extent the relative calm of modernstatistics is due to its domination by a vigorous school relatively well agreed within itself about the foundations.
The application ofstatistics in the process of science can be divided into three parts: (1) obtaining data (experiment and sampling design), (2) summarizing and describing data (exploratory data analysis, descriptivestatistics), and (3) using data from samples and experiments to make estimates and test competing hypotheses about the universe (inferentialstatistics).
2012 January, Robert L. Dorit, “Rereading Darwin”, inAmerican Scientist[1], volume100, number 1, archived fromthe original on14 November 2012, page23:
We live our lives in three dimensions for our threescore and ten allotted years. Yet every branch of contemporary science, fromstatistics to cosmology, alludes to processes that operate on scales outside of human experience: the millisecond and the nanometer, the eon and the light-year.
Sufficientstatistics for a given estimation problem are a collection ofstatistics or, equivalently, a collection of functions of the random sample, that summarize or represent all of the information in a random sample that is useful for estimating any.
2014 October 9, Marina Carver, “Study finds Boston police target African-Americans disproportionately”, inCNN[2]:
“Over the past month, the Department has held three separate meetings with the ACLU to receive feedback and engage the organization in the solutions,” the department said in a statement. “As a result of the meetings, the Department agrees that publishing FIOstatistics going forward is necessary, and the Department is working toward personalizing interactions between officers and citizens.”
