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A discipline, principally within applied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation of data.
Statistics is the only mathematical field required for many social sciences.
As for statistics, 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 of statistics 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 modern statistics is due to its domination by a vigorous school relatively well agreed within itself about the foundations.
The application of statistics 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, descriptive statistics), and (3) using data from samples and experiments to make estimates and test competing hypotheses about the universe (inferential statistics).
2012 January, Robert L. Dorit, “Rereading Darwin”, in American Scientist, volume 100, number 1, archived from the original on 14 November 2012, page 23:
We live our lives in three dimensions for our threescore and ten allotted years. Yet every branch of contemporary science, from statistics to cosmology, alludes to processes that operate on scales outside of human experience: the millisecond and the nanometer, the eon and the light-year.
A systematic collection of data on measurements or observations, often related to demographic information such as population counts, incomes, population counts at different ages, etc.
Sufficient statistics for a given estimation problem are a collection of statistics 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”, in CNN:
“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 FIO statistics going forward is necessary, and the Department is working toward personalizing interactions between officers and citizens.”