# Statistics

Statistics is a scientific discipline that deals with obtaining, ordering and analyzing a set of data in order to obtain explanations and predictions about observed phenomena.

Statistics consists of methods, procedures and formulas that allow collecting information and then analyzing it and drawing relevant conclusions from it. It can be said that it is Data Science and that its main objective is to improve the understanding of the facts from the available information.

The origin of the word statistics is usually attributed to the economist Gottfried Achenwall (Prussian, 1719-1772) who understood statistics as "science of things that belong to the State."

It should be noted that statistics is NOT a branch of mathematics. It uses tools of mathematics in the same way that physics, engineering or economics does, but that does not make them a part of mathematics. It is true that they are closely related, but statistics and mathematics are different disciplines.

## Transversality of statistics

One of the fundamental characteristics of statistics is its transversality. Its methodology is applicable to the study of various disciplines such as: biology, physics, economics, sociology, etc.

Statistics help to obtain relevant conclusions for the study of all types of agents such as: humans, animals, plants, etc. It generally does so through statistical samples.

## Statistical types

The types of statistics can be subdivided into two large branches: descriptive and inferential.

• Descriptive statistics: It refers to the methods of collection, organization, summary and presentation of a set of data. It is mainly about describing the fundamental characteristics of the data and for them indicators, graphs and tables are usually used.
• Inferential statistics: This is a step beyond mere description. It refers to the methods used to be able to make predictions, generalizations and obtain conclusions from the analyzed data, taking into account the degree of existing uncertainty.

Inferential statistics are subdivided into two large types: parametric and non-parametric statistics.

• Parametric statistics: It is characterized because it assumes that the data have a certain distribution or certain parameters are specified that should be fulfilled. Thus, for example, in a parametric analysis we can work under the assumption that the population is distributed as a Normal (we must justify our assumption) and then draw conclusions under the assumption that this condition is met.
• Non-parametric statistics: It is not possible to assume any type of underlying distribution in the data or a specific parameter. An example of this type of analysis is the binomial test.

## Origin and history of statistics

The history of statistics dates from before 3,000 BC. It was born with the objective of collecting information that the State needed, for example, on agriculture and trade.

In ancient Assyria and Egypt there is evidence of the collection of statistical data. Likewise, in Rome demographic data of the empire's inhabitants were collected, such as those of birth and mortality. This, with the purpose of making better decisions from the government.

Later, during the Middle Ages, statistics did not have great advances. However, in the Modern Age the first modern statistical census and the first table of probabilities of ages would be elaborated, both events in the seventeenth century. Then, towards the 20th century, mathematical tools from probability theory began to be incorporated into statistics. This, mainly due to the contributions of Kolmogorov and Borel.

Origin of statistics History of statistics

## Statistical objectives

The main objectives of the statistics are the following:

• Know the characteristics and make inferences or reach conclusions regarding a target population. This, usually from the analysis of a sample. This is typical of inferential statistics.
• It can allow establishing a relationship between different variables, finding the possible origin of a phenomenon, studying the changes in said event and making projections about it, if possible.
• Based on the conclusions obtained, decisions can be made, for example, if we are talking about a statistical study carried out by the Government to define a public policy.
• In the case of descriptive statistics, it allows to have a state of the art, that is, to know the characteristics of a database, for example, by calculating measures of central tendency such as the mean or the mode.
• It supports other disciplines such as economics, in the analysis and projection of indicators such as inflation or Gross Domestic Product. Likewise, in the field of biology, we have biostatistics that analyzes, in others, public health and environmental data.

## Statistical elements

The main elements of the statistic are:

• Population: Group of individuals that present or could present a common characteristic trait that we wish to investigate.
• Sample: It is a subgroup of data extracted from a population that must adequately represent the entire group.
• Parameters: These are measures that offer information about the center of a data set (measures of central tendency), others about the dispersion or variability (measures of dispersion) and others about the position of a value (measures of position such as percentiles).
• Experiment: Process or activity carried out intentionally to obtain a series of data or to confirm or refute a hypothesis.
• Variable: The characteristic or quality of a sample or population to which a value can be assigned.

## Example of the use of statistics in economics

Statistics are widely used in economic analysis. It helps us to check the application of economic theory in practice. Some examples of the use of statistics in economics are:

• Preparation of aggregate macroeconomic indicators.
• Predictions about the future behavior of demand.
• Test the validity of hypotheses based on economic theory.
• Calculate the unemployment rate.
• Organize and present economic data such as: price evolution, GDP, etc.

It is recommended to read:

• Random variable
• Simple random sample
Statistical inference

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