Some Aspects of Statistics

Abstract

The term statistics derives, as is well known, from the Latin ‘Status’ (state) and was originally used in connection with the description of the state of a country by means of a manifold of factual data characterizing this state. The characteristic of the state of a country, say, in relation to its population, is given by so-called statistical data (statistical material), which are obtained, for instance, by interviewing concrete people inhabiting the country (population census). These statistical data are then classified according to different features (properties) of the country’s inhabitants (sex, age, education, etc.) and are presented in the form of a summary indicating the distribution of the population according to the values of these properties, that is, the absolute or relative number of people (the absolute or relative measure of a set of people) belonging to each category accounted for (to each subset accounted for) of the country’s population (of the entire set of concrete people in the country). The initial statistical material is obtained by experimentation (interviewing the population), and the experimenters deal with each concrete person (each concrete object) separately. The classification of this experimental material leads to abstraction of the individual peculiarities of concrete persons and to the description of the state of the country’s population (or, in other words, the state of an abstract inhabitant of the country) with the aid of the measure of the set of concrete people belonging to different categories of the population. But by definition (see Sect. 1.5) the relative measure of a subset of concrete objects is the probability that the respective abstract object has the corresponding subset of values of the properties of these concrete objects. Therefore the classification of the statistical material leads, in this case, to the description of the state of an abstract inhabitant of the country by indicating the probability distribution for him to have different values of the properties of its inhabitants.