# Translations of Encyclopedia about Mathematics

## Stochastics

Stochastics comes from Greek estimation and studies mathematical procedures for examining random events. It concerns , and random selection and was first introduced by Jacob Bernoulli. Statistical laws are also important for market research or for estimating voting results, and are used in such scientific disciplines as the study of the spread of diseases.

The theory of games is a new field which studies the strategic behaviour of players, which can simulate outcomes in politics or economics. There are two binding game rules, although there is no certainty but only certain probabilities from which we can assume certain behaviours and outcomes.

Stochastic are used also in programming languages. When processing data, exactly set methods of generating random numbers with individual commands are used.

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## Statistics

The beginnings of statistics may be found in ancient times, from the Romans and other cultured nations. At that time, populations were counted, something which we find also in the bible. The word statistics comes from the Latin word of status (state). For a long period, statistics had a single task: to determine the state of a country at a certain point of time. Computers did not exist back then, for which reason much time was required to determine such information, unlike today.

It was only until the 17th and 18th centuries, during the period of absolutism, when statistics started to be developed as a separate science. However, by half way through the 20th century, most plans were not conceivable without this branch of science even though, up to that time, most statistics projects were counted by hand. After the Second World War, a transfer was made from strictly descriptional statistics to the analysis of statistical data and the study of statistical hypotheses using calculus of probabilities. This branch of statistics is also referred to as statistical mathematics.

Around this time, statistics also started to be used in , for example in quantum statistics, Boltsman’s statistics and thermodynamic statistics. Statistics is closely related to the fields of calculus of probabilities and . One of the most prominent joining links between statistics and probabilities is Gauss’s division or Gauss’s curve, which teachers use to assess a class according to individual marks.

Today, statistics is defined as a scientific method used for arithmetical-mathematical processing and for assessing mass phenomena. It plays an important role in planning and managing the economy, industry, trade, transport, in politics, in natural and humanitarian sciences, and in many other fields. Statistics is also used to present various results, used in bar graphs and circle diagrams or in multicoloured tables - all to help us understand the world around us. However, it is important that the individual results and calculations were made correctly and suitably interpreted. As with any other science, statistics operates on various fundamental rules and definitions.

In this manner, a summary of some observance or attempts conducted under identical conditions is called the whole, where the individual attempts or observations are called elements of the whole. If some random quantities or the variable x or y can be described within a whole as a distribution according to the function F(x), then we say that the aggregate distribution of F(x) has the variables x or y.

Statistics always concerns the final quantity of elements in a whole, or qualitative homogeneous elements referred to as a random selection which can have different sizes, depending on the size of the whole. The number of elements making up a random selection is referred to as the size of a random sample. The list then represents the determination of the exact number of discrete quantities. The most simple form of quantification when setting the percent occurrence of two events is yes – no. Presentation then most often uses a normal scale.

If objects or some factual content are compared and only the size of certain variables (“larger than”, “smaller than” or “same) is examined, we refer to it as order or value gradation. If studying the difference in sizes of individual objects, we require interval or unitary scales whose structure would be metric. In the strict meaning of the sense, graded scales are not interval scales because the same grades do not always have the same output and because the distance between the individual grades of this scale are not always the same.

When statistically processing empirical data, it must first be quantified, such as with a value scale which would be portrayable and measurable. By calculation we then determine the percent occurrence and, using value sets, we can set up a scale of values. By measurement, we determine the size. When calculating, we use basic numbers and, when setting up the value scale, we most often use ordinal or numerical numbers, which helps us compose a scale structure used to make an exact assessment.

With a set of ordinal numbers, the following can be assigned: median value, percentage share and correlation value. With interval scales, we can have arithmetical median value, standard deviation and correlation measurements.

For example, we can set the percentage occurrence distribution when rolling four dice. When throwing a total of 1300 dice (n), we can determine the number of thrown sixes.

Sixes                  0          1          2          3        4

Throws              627       499       151       20         3

In this case, the absolute percent occurrence (Hn) is 499. The relative percent occurrence hn