Statistics
Statistics is the science and practice of developing human knowledge through the use of empirical data. It is based soundly on statistical theory which is a branch of applied mathematics. Within statistical theory, randomness and uncertainty are modelled by probability theory. Statistical practice includes the planning, summarizing, and interpreting of uncertain observations. Because the aim of statistics is to produce the "best" information from available data, some authors make statistics a branch of decision theory.
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Origin
The word statistics comes from the modern Latin phrase statisticum collegium (lecture about state affairs), from which came the Italian word statista, which means "statesman" or "politician" (compare to status) and the German Statistik, originally designating the analysis of data about the state. It acquired the meaning of the collection and classification of data generally in the early nineteenth century. The collection of data about states and localities continues, largely through national and international statistical services; in particular, censuses provide regular information about the population.
Statistical methods
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 (experiment design),
 summarize a collection of observations to feature their commonality by suppressing details (descriptive statistics), and
 reach consensus about what the observations tell us about the world we observe (statistical inference).
In some forms of descriptive statistics, notably data mining, the second and third of these steps become so prominent that the first step (planning) appears to become less important. In these disciplines, data often are collected outside the control of the person doing the analysis, and the result of the analysis may be more an operational model than a consensus report about the world.
Probability
The probability of an event is often defined as a number between one and zero. In reality however there is virtually nothing that has a probability of 1 or 0. You could say that the sun will certainly rise in the morning, but what if an extremely unlikely event destroys the sun? What if there is a nuclear war and the sky is covered in ash and smoke?
We often round the probability of such things up or down because they are so likely or unlikely to occur, that it's easier to recognise them as a probability of one or zero.
However, this can often lead to misunderstandings and dangerous behaviour, because people are unable to distinguish between, e.g., a probability of 10^{4} and a probability of 10^{9}, despite the very practical difference between them. If you expect to cross the road about 10^{5} or 10^{6} times in your life, then reducing your risk of being run over per road crossing to 10^{9} will make you safe for your whole life, while a risk per road crossing of 10^{4} will make it very likely that you will have an accident, despite the intuitive feeling that 0.01% is a very small risk.
Use of prior probabilities of 0 (or 1) causes problems in Bayesian statistics, since the posterior distribution is then forced to be 0 (or 1) as well. In other words, the data is not taken into account at all! As Lindley puts it, if a coherent Bayesian attaches a prior probability of zero to the hypothesis that the Moon is made of green cheese, then even whole armies of astronauts coming back bearing green cheese cannot convince him. Lindley advocates never using prior probabilities of 0 or 1. He calls it Cromwell's Rule, from a letter Oliver Cromwell wrote to the synod of the Church of Scotland on August 5th, 1650 in which he said "I beseech you, in the bowels of Christ, consider it possible that you are mistaken."
Specialized disciplines
Some sciences use applied statistics so extensively that they have specialized terminology. These disciplines include:
 Biostatistics
 Business statistics
 Economic statistics
 Engineering statistics
 Statistical physics
 Demography
 Psychological statistics
 Social statistics (for all the social sciences)
 Process analysis and Chemometrics (for analysis of data from analytical chemistry and chemical engineering)
 Reliability engineering
Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make datadriven decisions. In these roles it is a key tool, and perhaps the only reliable tool.
See also
 Analysis of variance (ANOVA)
 Extreme value theory
 regression analysis
 List of academic statistical associations
 List of national and international statistical services
 List of statistical topics
 List of statisticians
 Machine learning
 Multivariate statistics
 Statistical phenomena
 List of publications in statistics
References
Lindley, D. Making Decisions. John Wiley. Second Edition 1985. ISBN 0471908088
External links
 Root Analysis Framework from CERN (Histogramms, Fits, ...)
 The R Project for Statistical Computing
 Statistics resources
 The Probability Web
 Virtual Laboratories in Probability and Statistics
 Statistics resources and calculators.
 Data, Software and News from the Statistics Community.
 Resources for Teaching and Learning about Probability and Statistics. ERIC Digest.
 Resampling: A Marriage of Computers and Statistics. ERIC/TM Digest.
 International Statistical Institute
 Free Statistical Software
 Free Statistical Tools on the WEB
 The Probability of Coincidence