Mathematical statistics is one of the main sections of a science such as mathematics, and is an industry that studies methods and rules for processing certain data. In other words, she explores ways to uncover patterns that are characteristic of large collections of identical objects, based on their selective examination.
The objective of this section is to build methods for estimating the probability or making a certain decision about the nature of developing events, based on the results. To describe the data, tables, diagrams, and also correlation fields are used. Probabilistic models are rarely used.
Mathematical statistics are used in various fields of science. For example, for the economy it is important to process information about homogeneous sets of phenomena and objects. They can be products manufactured by industry, personnel, profit data, etc. Depending on the mathematical nature of the results of observations, one can distinguish statistics of numbers, analysis of functions and time series, objects of non-numerical nature, multidimensional analysis. In addition, they consider general and particular (related to the restoration of dependencies, the use of classifications, selective research) tasks.
The authors of some textbooks believe that the theory of mathematical statistics is only a section of probability theory, others that it is an independent science with its own goals, objectives, and methods. However, in any case, its use is very extensive.
So, the most vivid mathematical statistics are applicable in psychology. Its use will allow the specialist to correctly substantiate the plans of the experiment, find the relationship between the data, summarize them, avoid many logical errors and much more. It should be noted that it is often simply impossible to measure a particular psychological phenomenon or personality trait without computational procedures. This suggests that the basics of this science are necessary. In other words, it can be called the source and base of probability theory.
The research method, which relies on the consideration of statistical data, is used in other areas. However, it should immediately be noted that its features as applied to objects of different nature of origin are always peculiar. Therefore, combining physical or socio-economic statistics into one science does not make sense. The general features of this method are reduced to counting a certain number of objects that are included in one or another group, as well as studying the distribution of quantitative features and applying probability theory to obtain certain conclusions.
Elements of mathematical statistics are used in such fields as physics, astronomy, etc. Here, the values of characteristics and parameters, hypotheses about the coincidence of any characteristics in two samples, distribution symmetry, and much more can be considered.
Mathematical statistics play a large role in conducting sample surveys. Their goal most often is to build adequate assessment methods and test hypotheses. Currently, computer technology is of great importance in this science. They allow not only to significantly simplify the calculation process, but also to create simulation modeling for the reproduction of samples or in studying the suitability of the results in practice.
In the general case, the methods of mathematical statistics help to draw two conclusions: either make the desired judgment about the nature or properties of the data being studied and their relationships, or prove that the results obtained are not enough to draw conclusions.