**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.

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.

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).

The probability of an event is often defined as a number between one and zero rather than a percentage. 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 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.

Some sciences use applied statistics so extensively that they have specialized terminology. These disciplines include:

- Biostatistics
- Business statistics
- Economic statistics
- Engineering statistics
- Population statistics
- Psychological statistics
- Social statistics (for all the
*social*sciences) - Process analysis and Chemometrics (for analysis of data from analytical chemistry and chemical engineering)

Links to observable statistical phenomena are collected at statistical phenomena

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2 See also 3 External links |

- Canada: Statistics Canada
- France: National Institute for Statistics and Economic Studies
- Greece: National Statistical Service of Greece
- India: Indian Statistical Institute
- New Zealand: Statistics New Zealand
- USA: American Statistical Association

Linear regression--analysis of variance (ANOVA) -- multivariate statistics -- extreme value theory -- list of statisticians -- list of statistical topics -- machine learning