Mathematical statistics for specialists in various fields

Mathematical statistics is one of the main sections of 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 sets of identical objects, based on their sample survey.

The purpose of this section is to build methods for estimating probability or making a definite decision about the nature of developing events, relying on the results obtained. To describe the data, tables, diagrams, and 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, data on profits, etc. Depending on the mathematical nature of the results of observations, one can select 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 studies) 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, tasks and methods. However, in any case, its use is very extensive.

Thus, the most clearly mathematical statistics are applicable in psychology. Its use will allow the expert to correctly substantiate the plans of the experiment, find the relationship between the data, generalize them, avoid many logical errors and much more. It should be noted that it is often impossible to measure this or that psychological phenomenon or personality property without computational procedures. This suggests that the basics of this science are necessary. In other words, it can be called the source and basis of probability theory.

The research method, which relies on the analysis of statistical data, is used in other areas. However, it should immediately be noted that its features in application to objects of different origin are always distinctive. Therefore, it is pointless to combine physical or socio-economic statistics into one science. The general features of this method are reduced to the calculation of a certain number of objects that belong to a particular group, as well as the study of the distribution of quantitative features and the application of probability theory to obtain certain conclusions.

Elements of mathematical statistics are used in such areas as physics, astronomy, etc. Here we can consider the values of characteristics and parameters, the hypotheses of the coincidence of any characteristics in two samples, the symmetry of distribution, and much more.

An important role is played by mathematical statistics in conducting selective surveys. Their goal is usually to build adequate assessment methods and test hypotheses. At present, computer technology is of great importance in this science. They make it possible not only to significantly simplify the calculation process, but also to create simulation simulations for multiplication of samples or when studying the suitability of the results obtained in practice.

In general, the methods of mathematical statistics help to draw two conclusions: either to take the desired judgment about the nature or properties of the data under study and their interrelations, or to prove that the obtained results are insufficient to draw conclusions.