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# Statistics

(statistics)

Statistics is the science and practice of developing human knowledge through the use of empirical data . It isbased on statistical theory which is a branch of applied mathematics . Within statistical theory, randomness and uncertainty aremodelled 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 statisticumcollegium (lecture about state affairs), from which came the Italian word statista, which means " statesman " or" politician " (compare to status ) andthe German Statistik, originally designating the analysis ofdata about the state. It acquired the meaning of the collection and classification of data generally in the early nineteenthcentury. 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 requiresus to

1. plan our observations to controltheir variability ( experiment design ),
2. summarize a collection of observations to feature theircommonality by suppressing details ( descriptivestatistics ), and
3. 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 secondand third of these steps become so prominent that the first step (planning) appears to become less important. In thesedisciplines, data often are collected outside the control of the person doing the analysis, and the result of the analysis may bemore an operational model than a consensus report about the world.

## Probability

The probability of an event is often defined as a number between one andzero. 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 thereis 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 torecognise 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 105 or 106 times in your life, then reducing your risk of being runover per road crossing to 10-9 will make you safe for your whole life, while a risk per road crossing of10-4 will make it very likely that you will have an accident, despite the intuitive feeling that 0.01% is a very smallrisk.

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 takeninto account at all! As Lindley puts it, if a coherent Bayesian attaches a prior probability of zero to the hypothesis that theMoon is made of green cheese, then even whole armies of astronauts coming back bearing green cheese cannot convince him. Lindleyadvocates 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 ofScotland on August 5th, 1650 in which he said "I beseech you, in the bowels of Christ, consider it possible that you aremistaken."

## Specialized disciplines

Some sciences use applied statistics so extensively thatthey have specialized terminology . These disciplinesinclude:

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systemsvariability, control processes (as in statisticalprocess control or SPC), for summarizing data, and to make data-driven decisions. In these roles it is a key tool, andperhaps the only reliable tool.