Statistics could be defined as the science that is responsible for collecting, organizing, processing, analyzing and interpreting data in order to deduce the characteristics of a target population, but this would only be a narrow vision of what this branch of knowledge comprises. The following is a very brief theoretical introduction to the broad concept of statistics.
Contents
What is statistics?
Statistics is the science that studies how information should be used and how to guide action in practical situations that involve uncertainty. (Gutiérrez, p.23)
Statistics is the science of data, which implies its collection, classification, synthesis, organization, analysis and interpretation, for decision-making in the face of uncertainty (Ángel, p. 28)
Statistics is the branch of human knowledge whose object is the study of certain inductive methods applicable to phenomena capable of quantitative expression. (López, p.1)
Statistics is the art of learning from data. It is related to the collection of data, its subsequent description and its analysis, which leads us to draw conclusions. (Ross, p.3)
Statistics is an exact science whose main objective is the study of various forms of behavior in society, for which it is based on the use of various methods and procedures mathematically demonstrable in a formal and rigorous way. (Condor, p.10)
Statistics is a science that facilitates decision-making through the orderly presentation of observed data in statistical tables and graphs, reducing the observed data to a small number of statistical measures that will allow comparison between different data series and estimating the probability of success of each of the possible decisions. (Fernández et.al, p.18)
Statistical objective
The goal of statistics is to improve understanding of facts from data. (Moore, p.267)
The main objective of statistics is to make inferences about a population, based on the information contained in a sample. (Pérez, p.172)
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In the following video, by Educatina, a short introduction to the concept of statistics is made, a definition is presented and, through an example, some additional concepts that will surely be useful to you.
What are the types of statistics?
There are basically two types of statistics, namely:
Descriptive statistics
Descriptive statistics can be defined as a method to describe numerous sets numerically. As it is a method of numerical description, it uses the number as a means to describe a set, which must be numerous, since statistical permanence does not occur in rare cases. It is not possible to draw concrete and precise conclusions from the statistical data. (Vargas, p.33)
Descriptive statistics objective
The ultimate purpose of descriptive statistics is to summarize information from more or less numerous sets of data. For this, it is based on an immediate concept to the counting task: the frequency, an empirical measure of the occurrence of the different states that a variable can present. (SGT, p.16)
Inferential, analytical or deductive statistics
Inferential statistics studies the probability of success of the different possible solutions to a problem in the different sciences in which it is applied and for this it uses the data observed in one or more samples of the population. By creating a mathematical model, she infers the behavior of the total population based on the results obtained in the observations of the samples. (Fernández et.al, p.17)
Objective of inferential statistics
Statistical inference attempts to make decisions based on the acceptance or rejection of certain relationships that are taken as hypotheses. This decision making is accompanied by a margin of error, the probability of which is determined. (Vargas, p.33)
Inferential statistics has two basic objectives; a) obtain valid conclusions about a population based on a sample, that is, that the conclusions that we obtain from a sample can be extrapolated to the population that gave rise to that sample and b) be able to measure the degree of uncertainty present in said inferences in terms of probability. (Díaz, p.287)
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Other definitions
Some of the most used terms in statistics are defined below:
Population. It is the set of all the possible elements that take part in an experiment or a study. There are two types
- Finite population. It is the one that indicates that it is possible to reach or exceed when counting. It is one that has or includes a limited number of measurements and observations. Infinite population. It is infinite if you include a large set of measurements and observations that cannot be reached in the count. They are infinite populations because hypothetically there is no limit to the number of observations that each of them can generate.
Sample. A set of measurements or observations taken from a given population. It is a subset of the population.
Representative sample. A representative subset selected from a population from which it was obtained.
Sampling. To the study of the representative sample.
Census. To the complete study of the population.
Parameter. It is made up of measurable characteristics in a complete population. It is assigned a symbol represented by a Greek letter.
Statistician or statistician. It is the measure of a characteristic relative to a sample. Most sample statistics are found by means of a formula and are often assigned symbolic names that are Latin letters.
Statistical data (Variables). The data are groupings of any number of related observations. To be considered a statistical data, it must have 2 characteristics: a) That they are comparable to each other. b) That they have some relationship.
Variable. A characteristic that assumes values.
Data classes
- Quantitative or scalar variable. It will be a variable when you can assume its results in numerical measures. Discrete quantitative variable. It is one that can assume only certain values, integers. Example: The number of students (1,2,3,4) Continuous quantitative variable. It is one that can theoretically take any value on a scale of measurements, be it integer or fractional. Example, Height: 1.90 m Nominal qualitative variables. When it is not possible to make numerical measurements, they are susceptible of classification. Example: Color of cars: red, green, blue.
Experiment. It is a planned activity, the results of which produce a set of data. It is the process by which an observation or measurement is recorded. Example: What will be the consumer's preference for two soft drink brands with similar characteristics in a harmonious environment and without advertising?
Descriptive statistics video course
Here is a descriptive statistics course through which you can learn the fundamental concepts of this science (José Luis Suárez, 13 videos)
Bibliography
- Ángel Gutiérrez, Julio César. Applied general statistics. Eafit University, 1998. Condor E., Ilmer. Theory of probability and statistical applications.Díaz Narváez, Víctor. Methodology of scientific and biostatistical research. RIL Editores, 2009 Fernández Fernández, Santiago; Cordero Sánchez, José María; Córdoba Largo, Alejandro; Lamb, José María. Descriptive statistics, ESIC Editorial, 2002. Gutiérrez Cabria, Segundo. Philosophy of Statistics, Universitat de València, 1994 López Cazuzo, Rafael. Calculus of probabilities and statistical inference, Andrés Bello Catholic University, 2006. Moore, David S. Basic applied statistics, Antoni Bosch editor, 2005. Pérez Tejada, Arnoldo Elorza. Statistics, social, behavioral and health sciences. Cengage Learning Editors, 2008 Ross, Sheldon M. Introduction to Statistics,Editorial Reverté, 2007.SGT. Statistics and probability in compulsory secondary education, Ministry of Education, 2003, Vargas Sabadías, Antonio. Descriptive and inferential statistics, University of Castilla La Mancha, 1996.
