Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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# ProbabilityAndStatistics

```: back to MathematicsAndStatistics

: ProbabilityAxioms -- ProbabilityTheory
: ProbabilityApplications -- ProbabilityDistributions

: StatisticalTheory
: PlanningResearch -- SummarizingStatisticalData -- InterpretingStatisticalData

Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. In any case, we measure the uncertainty of '''events''' on a scale from zero (impossible events) to one (certain events or no uncertainty).

ProbabilityAxioms form the basis for mathematical ProbabilityTheory. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. ProbabilityApplications include even more than Statistics, which is usually based on the idea of ProbabilityDistributions.

ProbabilityTheory plays a critical role in the development of StatisticalTheory. Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to
#plan our observations to control their variability (PlanningResearch),
#summarize a collection of observations to feature their communality by suppressing details (SummarizingStatisticalData), and
#reach consensus about what the observations tell us about the world we observe (InterpretingStatisticalData).

There are some ScienCes which use statistics so extensively that we recognize special disciplines like:
#BioStatistics (including MedicalStatistics)
#PsychologicalStatistics