STATISTICS. - This term probably derives from the Latin *status*, which means state, position, condition, or manner of being. It was first used in Italy in 1589 by Ghilini, and later by Achenwall and others to denote the science that describes and examines the most notable aspects of the State.
Today, the term *statistics* is commonly used to refer to a collection of numerical data concerning phenomena susceptible to enumeration and measurement, such as, for example, the clergy, production statistics, student statistics, etc. However, in a scientific sense, statistics is regarded as "a technique suitable for the quantitative study of mass or collective phenomena, where mass or collective phenomena are understood as those phenomena (physical, biological, social) whose measurement requires a mass or collection of observations of other simpler phenomena called individual or single phenomena" (Gini).
In this sense, statistics serves to study reality—both the natural and social worlds—in its phenomenal aspects, understood not as individual cases or facts, but as a set of cases or facts susceptible to observation. It helps to discover relationships, regularities, and laws that are difficult to deduce from individual or few observations.
To the statistics in this scientific sense, the attribute *methodological* is often given to distinguish it from *applied statistics*, which studies concrete collective phenomena using the procedures indicated by methodological statistics. This distinction is merely a practical division (similar, for example, to the distinction between theoretical physics and experimental physics) to allow for the autonomous development of theoretical frameworks on one hand, and a deeper exploration of specific phenomena on the other.
I. Historical Notes
Ancient documents show that from the formation of the earliest human societies, systems were used to enumerate both the elements composing these societies (families, individuals, men fit for military service, etc.) and the goods they possessed (livestock, hunting products, etc.).The Church itself felt the need for such records for its spiritual purposes and, one might almost say, established from its origins the registration of births and deaths. Indeed, the Council of Trent (Session XXIV, *De reform.*, c. 1) made it obligatory for parish priests to keep up-to-date records of births, deaths, and marriages, and it is precisely from these sources that scholars today generally draw to study the demographic conditions of past centuries (see PARISH REGISTERS).
Enumerations were evidently the basis for administrative and political investigations. However, by the mid-17th century, the description of notable aspects of the State took on an organic form in studies of independent interest. Scientific statistics thus originated. Vitus Seckendorff (1626–92), Hermann Conring (1600–81), and Gottfried Achenwall (1719–72) can be considered representatives of the so-called German university statistics. Simultaneously, in England, the approach known as that of the political arithmeticians developed, which, from numerical data, sought to derive empirical laws governing social phenomena. This approach thus had an investigative character, in contrast to the German one, which was descriptive. The most notable representatives of this school are John Graunt (1620–74) and William Petty (1635–87) for population phenomena, Gregory King (1648–1712) and Charles Davenant (1656–1714) for economic phenomena, and the astronomer Edmond Halley (1656–1742) for what is now called the insurance branch, having constructed a mortality table for the inhabitants of Breslau. A particularly important development followed in the field of population statistics, which can be said to have reached maturity with the work of Johann Peter Süssmilch (1707–67): *Die göttliche Ordnung in den Veränderungen des menschlichen Geschlechts*. This author attributed to divine order the fact that births exceed deaths and that the sex ratio remains almost constant (hovering, according to later studies, around 105 or 106 males for every 100 females at all times and in all places). However, as Villani reports in his chronicles, this phenomenon of higher male birth rates had already been observed and recorded three or four centuries earlier in the baptistery of San Giovanni in Florence, through a systematic examination of baptismal records.
The English school’s approach is connected to the mathematical-encyclopedic direction, particularly developed in France by eminent mathematicians such as B. Pascal (1623–62), J. Bernoulli (1654–1705), A. De Moivre (1667–1754), and P. S. Laplace (1749–1827), who applied
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**THE SCOPE OF STATISTICS**
IV. MEASURING THE INTENSITY OF A COLLECTIVE PHENOMENON
The data obtained from statistical surveys do not always lend themselves to providing a synthetic understanding of a phenomenon or to enabling a comparison of that phenomenon with others. For example, the differing prices obtained in the various Italian markets of a region for the same quantity of goods do not, in their raw form, lend themselves to making a synthetic comparison with the prices of other goods or to studying the variations that the price of that type of goods undergoes over time. It is therefore necessary to know how to synthesize all these raw figures into a single value that measures the intensity of the phenomenon: this is called the average value. Even our minds, in certain circumstances, summarize different impressions into a more synthetic one; the mathematical method has the advantage of making this determination more objective. However, it can be done in different ways, each corresponding to specific requirements, yielding different average values, with different names, the principal ones being: simple arithmetic mean, weighted arithmetic mean, simple and weighted geometric mean, harmonic mean, median, normal value or mode or prevalent value, power means, etc.Once the average intensity of a collective phenomenon has been determined, it may be of practical and scientific interest to measure its variability, that is, the tendency of phenomena to assume different modalities. It is clear, in fact, that often it is not enough to know the average wealth of the inhabitants of two regions; it may also be of interest to know the inequality existing among these inhabitants. In two towns A and B, the average wealth may be identical, but the distribution of this wealth among the inhabitants may be very different in A and B. The same can be said of wages, heights, etc., which in A may be almost equal among all individuals, while in B they may differ greatly from one individual to another.
Statistics has developed appropriate measures called indices of variability. The principal ones are: range, mean absolute deviation, standard deviation, mean difference, and concentration ratio. The latter measure is of great importance in the economic and social field for comparing the varying degrees of inequality in the distribution of income, wealth, assets, etc., across different regions.
V. STATISTICAL RATIOS AND RELATIONS
When a logical connection exists between two collective phenomena or between a collective phenomenon and a non-collective one (such as between wealth and population, legitimate births and married women, population and territory, deaths from a specific cause and total deaths, etc.), a statistical ratio can be established between the intensities of the two phenomena, generally expressed as a percentage.
The principal types are: ratio of composition and part to whole, ratio of derivation, index ratio or index number, ratio of coexistence, ratio of duration, and ratio of repetition. At times, however, it is of interest to see whether the modalities of one phenomenon are sensitive to the quantitative or qualitative manifestations of another. For example, it may be of interest to see whether the modalities of height depend on those of profession, or whether the modalities of income are related to those of assets, etc. The study of this aspect falls under the heading of research into the relation between two phenomena (more precisely, between the modalities of two phenomena). This can be approached from different angles. For example, by comparing two distributions globally, one can observe concomitance, transvariation, dissimilarity, asymmetry, antitransvariation, etc. By comparing individual modalities, one can instead measure the degree of connection or dependence, the degree of concordance or correlation, for which statistics has developed various appropriate indices.
Other important chapters of statistics include: the integration of data (developing methods to eliminate or correct gaps, errors, and causes of non-representativeness in the data); the comparability of data (to eliminate intrinsic and extrinsic causes that sometimes make direct comparisons between statistical data erroneous); and finally, the logic of statistics, which, through an in-depth examination of the various phases of scientific research and the symptomatology of causes, leads to the formulation of laws and the prediction of future collective phenomena, this being the ultimate aim of statistics.
VI. APPLIED STATISTICS
The application of statistical method to the study of particular classes of phenomena has given rise to separate disciplines such as demographic statistics or demography, biometrics, anthropometry, economic statistics or econometrics, and social statistics, which in turn includes judicial statistics, moral statistics, health statistics, labor statistics, intellectual statistics, religious statistics, etc.A brief overview of some of these branches is given here, with references to the respective entries for demographic statistics or demography (v.), biometrics (v.), and anthropometry.
### Physical Science
A decisive contribution has been made by statistics to modern physics, where it has enabled enormous progress previously unimaginable before its introduction into this science. The branches that have benefited most are the kinetic theory of gases, thermodynamics (v. THERMODYNAMICS), quantum theory (v. QUANTUM THEORY), and theories on the nature and structure of the atom.
### Economic or Econometric Science
This discipline studies, using statistical methods, the phenomena of production, exchange, and consumption. It thus provides for the collection and analysis of data concerning industrial, mining, and agricultural production; wholesale and retail trade, both domestic and international; the prices of goods and services; household budgets; the cost of living; wages; the financial and banking market; railway, road, maritime, and air traffic; income; wealth; etc., in order to gain precise knowledge of the phenomena arising from human activity aimed at satisfying their needs. These phenomena are often related to demographic and social phenomena to illustrate the life and economic evolution of a country.
### Social Science
This discipline studies various classes of phenomena connected with the social life of human groups. Some of these classes of phenomena tend to form separate disciplines, and brief notes are given on them:
a) **Judicial Science** — Its object is the quantitative study of both the activity of state organs aimed at restoring violated rights or resolving disputes, and the persons, matters, and acts to which this activity refers (Spallanzani). It distinguishes:
a) criminal judicial science (crimes against persons, property, public morals, criminality, reformatories, etc.);
b) civil judicial science (litigiousness, personal separations of spouses, notarial acts, etc.);
c) commercial judicial science (bankruptcies, bill protests, etc.).
b) **Moral Science** — Quantitatively studies phenomena related to customs and morality in general, such as alcoholism, prostitution, begging, etc.
c) **Health Science** — Includes research related to morbid forms of a social nature (tuberculosis and other infectious diseases, the mentally ill, etc.). It assists, without sanitary and hospital care, centers for the diagnosis and treatment of malignant tumors, health services, etc.
d) **Labor Science** — Studies phenomena concerning employment and unemployment, labor remuneration, strikes and lockouts, internal labor migrations, trade unions, etc.
e) **Intellectual Science** — Concerns:
a) phenomena in the educational field, such as enrollments, examinations, promotions, graduations, teachers of all types and levels of schools;
b) the activity of academies, libraries, art galleries, archives, etc.;
c) shows and radio;
d) the press, copyright, etc.
### Religious Science
This concerns the quantitative study of phenomena directly or indirectly related to religion. It thus includes, on the one hand, phenomena arising from the spiritual and social activity of individual Churches, and, on the other, all those social phenomena not strictly religious which are, however, subject to varying degrees of religious influence. The very different characteristics of these two groups of phenomena lead to a division of religious science into two parts: ecclesiastical science and confessional science.
### Ecclesiastical Science
Among the branches of social science, this can be said to have been, until recently, the most neglected, mainly due to a lack of documentary material. Some proposals made by the Central Statistical Board in 1872 and 1879 to conduct an extensive survey of:
a) persons engaged in worship and the population;
b) objects related to worship, such as buildings, sacred furnishings, property of ecclesiastical institutions, tithes, collections, offerings, etc.;
c) acts related to worship,
were not implemented because it is evident that to record phenomena related to the life of the Church, its administration, and religious practices, an organ directly dependent on the Holy See is required.
A significant flourishing of studies in ecclesiastical science occurred in Italy around 1940. The most important topics for which studies are available include:
- the numerical consistency of secular clergy, religious men and women in Italy from 1881 to 1936;
- the average age of missionaries and clergy residing in Italy;
- the longevity of Princes of the Church;
- parish rural property;
- the age of children at Baptism;
- the frequency of the Sacraments, etc.
The *Annuario Pontificio*, which since 1944 has begun publishing various statistical data, paves the way for a more systematic and organized knowledge of phenomena that properly pertain to the field of ecclesiastical science.
### Confessional Science
This particularly studies the demographic and socio-economic aspects of