THE BRANCHES OF STATISTICS, WHAT THEY STUDY AND APPLICATIONS - DUDAS - 2025

The statistics is a branch of mathematics, which corresponds to the collection, analysis, interpretation, presentation and organization of data (value set qualitative or quantitative variable). This discipline seeks to explain the relationships and dependencies of a phenomenon (physical or natural).

The English statist and economist Arthur Lyon Bowley, defines statistics as: "Numerical statements of facts from any research department, situated in relation to one another." In this sense, statistics is responsible for studying a certain population (in statistics, a set of individuals, objects or phenomena) and / or mass or collective phenomena.

This branch of mathematics is a transversal science, that is, applicable to a variety of disciplines, ranging from physics to social sciences, health sciences, or quality control.

In addition, it is of great value in business or government activities, where the study of the data obtained makes it possible to facilitate decision-making or make generalizations.

A common practice to carry out a statistical study applied to a problem is to start by determining a population, which can be of different subjects.

A common example of population is the total population of a country, therefore, when a national population census is carried out, a statistical study is being carried out.

Some specialized disciplines of statistics are: Actuarial Sciences, Biostatistics, Demography, Industrial Statistics, Statistical Physics, Surveys, Statistics in the Social Sciences, Econometrics, etc.

In psychology, the discipline of psychometry, which specializes in and quantifying psychological variables typical of the human mind, using statistical procedures.

Main branches of statistics

Statistics is divided into two large areas: descriptive statistics and inferential statistics, which comprise applied statistics.

In addition to these two areas, there is mathematical statistics, which comprises the theoretical bases of statistics.

1- Descriptive statistics

The descriptive statistics is the branch of statistics describing summarized quantitatively or (measurable) features a collection of a collection of information.

That is, descriptive statistics is responsible for summarizing a statistical sample (set of data obtained from a population) instead of learning about the population that the sample represents.

Some of the measures commonly used in descriptive statistics to describe a data set are measures of central tendency and measures of variability or dispersion.

As for the measures of central tendency, measures such as the mean, the median and the mode are used. While variance, kurtosis, etc. are used in the variability measures.

Descriptive statistics is usually the first part to perform in a statistical analysis. The results of these studies are usually accompanied by graphs, and they represent the basis for almost any quantitative (measurable) analysis of data.

An example of a descriptive statistic might be to consider a number to summarize how well a baseball batter is performing.

Thus, the number is obtained by the number of hits that a batter has given divided by the number of times he has been at bat. However, this study will not give more specific information, such as which of those hits have been home runs.

Other examples of descriptive statistics studies can be: The average age of citizens living in a certain geographic area, the average length of all books referring to a specific topic, the variation with respect to the time that visitors spend browsing a Internet page.

2- Inferential statistics

The inferential statistics differs descriptive statistics mainly by the use of inference and induction.

That is, this branch of statistics seeks to deduce properties of a studied population, that is, it not only collects and summarizes the data, but also seeks to explain certain properties or characteristics from the data obtained.

In this sense, inferential statistics implies obtaining the correct conclusions from a statistical analysis carried out using descriptive statistics.

For this reason, many of the experiments in social sciences involve a small population group, thus through inferences and generalizations it can be determined how the general population behaves.

The conclusions obtained through inferential statistics are subject to randomness (absence of patterns or regularities) but by applying the appropriate methods, relevant results are obtained.

Thus, both descriptive statistics and the inferential statistics go hand in hand.

Inferential statistics is divided into:

Parametric statistics

It includes statistical procedures based on the distribution of real data, which are determined by a finite number of parameters (a number that summarizes the amount of data derived from a statistical variable).

To apply parametric procedures, for the most part, it is required to previously know the form of distribution for the resulting forms of the studied population.

Therefore, if the distribution followed by the data obtained is completely unknown, a non-parametric procedure should be used.

Nonparametric statistics

This branch of inferential statistics comprises the procedures applied in statistical tests and models in which their distribution does not conform to the so-called parametric criteria. As the data studied define its distribution, it cannot be previously defined.

Non-parametric statistics is the procedure that should be chosen when it is not known whether the data fit a known distribution, so that it can be a step prior to the parametric procedure.

Likewise, in a non-parametric test, the chances of error are reduced by using adequate sample sizes.

3- Mathematical statistics

The existence of Mathematical Statistics has also been mentioned as a discipline of statistics.

This consists of a previous scale in the study of statistics, in which they use the theory of probability (branch of mathematics that studies random phenomena) and other branches of mathematics.

Mathematical statistics consists of obtaining information from data and uses mathematical techniques such as: mathematical analysis, linear algebra, stochastic analysis, differential equations, etc. Thus, mathematical statistics have been influenced by applied statistics.

References

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