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Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis , linear algebra , stochastic analysis , differential equations , and measure theory .
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, [5] or as a branch of mathematics. [6] Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data ...
Operations research (or operational research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems; Management science focuses on problems in the business world.
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory. Statisticians generate data with random sampling or randomized experiments .
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Probability and statistics are two closely related fields in mathematics, sometimes combined for academic purposes. They are covered in several articles: Probability; Statistics; Glossary of probability and statistics; Notation in probability and statistics; Timeline of probability and statistics
Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality.