STATISTICS. The word "statistic" is derived from the Latin status, which, in the so-called Middle Ages, had come to mean a "state " in the political sense. "Statistic," therefore, originally denoted inquiries into the condition of a state. Since the beginning of the 18th century the denotation of the word has been extended so as to include subjects only indirectly connected with political organizations, while at the same time the scope of the investigations it implies has become more definite, and at the present day may be said, for practical purposes, to be fixed, though there are still controversies as to the position of statistical studies in relation to other departments of scientific procedure.

.History. - The origin of what is now known as " statistic" (Ger. Die Statistik ; Fr. La Statistique; Ital. Statistica) can only be referred to briefly here. As M. Maurice Block has observed in commencing his admirable treatise, "it is no exaggeration to say that statistic has existed ever since there were states." For the first administrative act of the first regular Government- was probably to number its fighting men, and its next to ascertain with some degree of accuracy what amount of taxation could be levied on the remainder of the community. As human societies became more and more highly organized, there can be no doubt that a very considerable body of official statistics must have come into existence, and been constantly used by statesmen, solely with a view to administration. The Romans, who may be described as the most business-like people of antiquity, were careful to obtain accurate information regarding the resources of the state, and they appear to have carried on the practice of taking the census, a very comprehensive statistical operation, with a regularity which has hardly been surpassed in modern times. As to the efficiency of the work done we have unfortunately very little information, but those who are curious on the subject may be referred to an article by Dr Hildebrand, entitled "Die amtliche Bevolkerungsstatistik im alten Rein," printed in the Jahrbuch fur Nationalokono2nie and Statistik, 1866, p. 82.

Statistics, or rather the material for statistics, therefore existed at a very early period, but it was not until within the last three centuries that systematic use of the information available began to be made for purposes of investigation and not of mere administration. According to M. Block, the earliest work in which facts previously known only to Government officials were published to the world was a volume compiled by Francesco Sansovino, entitled Del Governo et A m2ninistrazione di Diversi Regni et Republiche, which was printed in Venice and bears the date 1583. Other works of a similar kind were published towards the end of the 16th century in Italy and France. Regarding these and other early books on the subject reference may be made to Fallati's Einleitung in die Wissenschaft der Statistik, Dr G. B. Salvioni's preface and notes to his translation into Italian of Dr Mayes work on statistics, and other authors mentioned at the close of this article.

Works on state administration and finance continued to be published during the first half of the 17th century, and the tendency to employ figures, which were hardly used at all by Sansovino, became more marked, especially in England, where the facts connected with " bills of mortality" had begun to attract attention.

In the year 1660 Hermann Conring, "professor of medicine and politics," a rather odd combination, in the university of Helmstiidt, was in the habit of giving lectures in which he analysed and discussed the circumstances existing in various countries, in so far as they affected the happiness of the inhabitants. Conring's example was followed by other writers, in Germany and elsewhere, to whom reference is made by Block (Traite, pp. 5, 6) and Haushofer (Lehr- and Handbuch, p. 10, note).

The best-known member of the "descriptive" school was Achenwall (1719-1772), who is sometimes spoken of as "the father of modern statistics," but, as his procedure was essentially the same as that of Conring, though it was carried out more fully, the title has not been unanimously granted. It is generally admitted, however, that Achenwall's work gave a great impulse to the pursuit of the studies which are now included under the title of statistics. He called his book Staatsverfassung der europluschen Reiche in the first two editions (1749, 1752), meaning "Constitution of the States of Europe." Subsequently he added " vornehmsten " and then "heutigen " before " europaischen," evidently with the desire of bringing his work, which may be regarded as the germ of such volumes as the Statesman's rear-Book, "up to date." Achenwall is usually credited with being the first writer who made use of the word "statistics," which he applied to his collection of "noteworthy matters regarding the state" (Staatsmerkwiircligkeiten), but the claim has been disputed procure evidence in favour of a particular system of by M. Block, who points out that the term colleyzum thought were not slow to follow. M. Block makes the statisticunt had been previously employed by Schmeitzel, a following remarks on the influence exercised on his con-follower of Conring, whose lectures at Jena were no doubt temporaries by the work of Sussmilch : - " If the author of attended by Achenwall. the Gottliche Ordnung had been a professor his influence In any case statistics, in the modern sense of the word, would have been much greater than it was. In maintain-did not really come into existence until the publication by ing that the movement of population is subject to law, J. P. Stissmilch, a Prussian clergyman, of a work entitled that there is a regularity in the recurrence of such phenoDie gottliche Ordnung in den Veranderungen des Mensch- mena which allows of their being foreseen, he cast into the lichen. Geschlechts aus dent Geburt, dem Tode, and der public mind a leaven which has evidently contributed to Fortpflanzung desselben erwiesen. In this book a system- the progress of science." Although for many years after atic attempt was made to make use of a class of facts the appearance of Siissmilch's book there was a good deal which up to that time had been regarded as belonging to of resistance to the introduction of " arithmetic " as the "political arithmetic," under which description some of coadjutor of moral and political investigations, yet, practithe most important problems of what modern writers term tally there was a tacit admission of the usefulness of "vital statistics" had been studied, especially in England. figures, even by the chiefs of the so-called " descriptive " Siissmilch had arrived at a perception of the advantage of school. On the other hand Sfissmilch's success was the studying what Quetclet subsequently termed the "laws of origin of a " mathematical " school of statisticians, some of large numbers." He combined the method employed by whom carried their enthusiasm for figures so far that they the Conring-Achenwall school of "descriptive statistics," refused to allow any place for mere " descriptions " at all. whose works were not unlike modern school-books of geo- These two schools have now coalesced, each admitting the graphy, with that of the "political arithmeticians," who importance of the point of view urged by the other. They had confined themselves to investigations into the facts were, however, still perceptibly distinct even as late as regarding mortality and a few other similar subjects, 1850, and the ignorant hostility with which many people without much attempt at generalizing from them. even among the cultivated classes still regard statistical Political arithmetic had come into existence in England inquiries into the nature of human society may be rein the middle of the 17th century, or about the time garded as a survival of the much stronger feeling which when Conring was instructing the students of Helmsthdt. showed itself among "orthodox" professors of law and The earliest example of this class of investigation is the economics on the publication of Siissmilch's treatise. work of Captain John Graunt of London, entitled Natural M. Block is of opinion that the descriptive school, by and Political Annotations made upon the Bills of Mortality, whom figures are regarded merely as accessories to and which was first published in 1666. This remarkable illustrations of the text, would have maintained its position work, which dealt with mortality in London only, ran even now but for the establishment of official statistical through many editions, and the line of inquiry it sug- 'offices and the influence of the great Belgian Qnetelet. gested was followed up by other writers, of whom the Quetelet's work was certainly " epoch-making" in a far most distinguished was Sir William Petty, whose active higher degree than that of any of his predecessors. To mind was naturally attracted by the prospect of making the impulse created by him must be attributed the foundause of a new scientific method in the class of speculations tion in 1835 of the Statistical Society of London, a body which occupied him. Sir William was the first writer to which, though it has contributed little to the discussion of make use of the phrase which for nearly a century after- the theory of statistics, has had a considerable and very wards was employed to describe the use of figures in the useful influence on the practical work of carrying out investigation of the phenomena of human society. He statistical investigations in the United Kingdom and called his book on the subject, which was published elsewhere. Quetelet's works were numerous and multi-in 1683, Five Essays in Political Arithmetick. Other farious, but his most important contribution to the growth of writers, of whom Halley, the celebrated mathematician statistical inquiry was his investigation of the theory of pro-and astronomer, was one, entered on similar investigations, babilities as applied to the "physical and social" sciences, and during the greater part of the 18th century the num- contained in a series of letters to the duke of Saxe-Coburg ber of persons who devoted themselves.to "arithmetical" and Gotha, and published in 1846. Quetelet was above inquiries into problems of the class now known as statis- all things an exponent of the "laws of large numbers." tical was steadily increasing. Much attention was given He was especially fascinated with the tendency to relative to the construction of tables of mortality, a subject which constancy of magnitude displayed by the figures of moral had a great attraction for mathematicians, who were eager statistics, especially those of crime, which inspired him to employ the newly-discovered calculus of probabilities on with a certain degree of pessimism. His conception of concrete problems. Besides Halley, De Moivre, Laplace, an average man (l'homme moyen) and his disquisition on and Euler busied themselves with this branch of study. the "curve of possibility" were most important contribuAttempts were also made to deal with figures as the tions to the technical development of the statistical basis of political and fiscal discussion by Arthur Young, method, though, as M. Block observes, their value may Hume, and other historical writers, as well as by the two have been somewhat exaggerated by subsequent. writers Mirabeaus. (Block, ch. i. p. 16, and ch. v. p. 112 sq.). It is not It is now necessary to return to Siissmilch, who, as possible to enter at length into Quetelet's work in con-already mentioned, endeavoured to form a general theory nexion with statistical science. At the close of this article of society, based on what were then termed " arithmetical " will be found a list including those of his works which are premisses, treated nearly on the lines laid down by Achen- likely to be of use to students of statistics.

of statistics as well as a statistical method. It is true that a few books were published between 1830 and 1850 in which the politico-geographical description of a country is spoken of as " statistics," which is thus distinguished from "political arithmetic." The title of Knies's great work, Die Statistik als selbstiindige Wissenschaft (Cassel, 1850), is especially noteworthy as showing that the nature of the controversy was changing. The opponents of Siissmilch maintained that "political arithmetic" ought not to be spoken of as statistics at all. They clung to the conceptions of Conring and Achenwall, to whom " statistics " represented " Staatenkunde " or " Staatszustand skunde," or, as Herzberg, one of Achenwall's followers, called it, "die Kenntniss von der politischen Verfassung der Staaten." Knies claimed that the really " scientific " portion of statistics consisted of the figures employed. As Haushofer says, "his starting point is political arithmetic."

Some eminent statisticians of the latter half of the present century agree with Knies, but the majority of the modern writers on the theory of statistics have adopted a slightly different view, according to which statistics is at once a science relating to the social life of man and a method V investigation applicable to all sciences. This view is ably maintained by Mayr, Haushofer, Gabaglio, and Block, who may be taken to represent the opinions held by the majority of statisticians on the Continent.

Having dealt as far as was possible, within the limits of this article, with the history of statistics, we may here, enter a little more minutely into the views of the existing Continental school. This is all the more necessary because, singular to say, there has been no systematic exposition of the subject in England. Isolated dicta have been furnished by high authorities, such as the late Dr W. A. Guy, Prof. Ingram, Sir Rawson W. Rawson, Mr Robert Giffen, and to some extent also by John Stuart Mill, Buckle, Sir George Cornewall Lewis, and other historical and economic writers. There are also monographs on particular points connected with the technique of statistical investigation, such as the contribution made by Mr F. Y. Edgeworth to the discussions at the jubilee of the Statistical Society in 1885, and some of the observations contained in a paper by Mr Patrick Geddes, entitled An Analysis of the Principles of Economics, read before the Royal Society of Edinburgh in 1884. Prof. Foxwell has also lectured on the subject of statistics in his capacity of Newmarch lecturer at University College, London. But there has been no attempt to deal with the subject in a systematic way. The practice of statistical inquiry, on the other hand, has been carried on in England with a high degree of success.

With regard to the few invasions of the domain of theory attempted by English writers, it may be observed that the authorities above mentioned are not unanimous. Dr Guy as well as Sir Rawson Rawson, who handled the subject with great ability at the jubilee meeting of the London Statistical Society in June 1885, both claim that statistics is to be regarded as an independent science, apart from sociology, while Prof. Ingram, who presided over Section F at the Dublin meeting of the British Association in 1878, maintained that statistics cannot occupy a position co-ordinate with that of sociology, and went on to say that they " constitute only one of the aids or adminicula of science." Mr Giffen has also expressed himself adversely to the Continental doctrine that there is an independent science of statistics, and this opinion appears to be the correct one, but, as Dr Guy and Sir Rawson Rawson have the support of the great body of systematic teaching emanating from distinguished Continental statisticians in support of their view, while their opponents have so far only the ()biter dicta of a few eminent men to rely upon, it appears needful to examine closely the views held by the Continental authorities, and the grounds on which they are based.

The clearest and shortest definition of the science of statistics as thus conceived is that of M. Block, who describes it as "la science de l'homme vivant en societe en taut qu'elle pent etre exprimee par les chiffres." He proposes to give a new name to the branch of study thus defined, namely, " Demography." Mayes definition is longer. He defines the statistical science as " die systematische Darlegung und Erorterung der thatsachlichen \Tor-gang° und der aus diesen sich ergebenden Gesetze des gesellschaftlichen menschlichen Lebens auf Grundlage quantitativer Massenbeobachtungen" (the systematic statement and explanation of actual events, and of the laws of man's social life that may be deduced from these, on the basis of the quantitative observation of aggregates). Gabaglio's view is practically identical with those adopted by .Mayr and Block, though it is differently expressed. He says "statistics may be interpreted in an extended and in a restricted sense. In the former sense it is a method, in the latter a science. As a science it studies the actual social-political order by means of mathematical induction."

This discussion regarding the nature of statistics is to a large extent a discussion about names. There is really no difference of opinion among statistical experts as to the subject-matter of statistics, the only question being - Shall statistics be termed a science as well as a method ? That there are some investigations in which statistical procedure is employed which certainly do not belong to the domain of the supposed statistical science is generally admitted. But, as already shown, an attempt has been made to claim that the phenomena of human society, or some part of those phenomena, constitute the subject-matter of an independent statistical science. It is not easy to see why this claim should be admitted. There is no reason either of convenience or logic why the use of a certain scientific method should be held to have created a science in one department of inquiry, while in others the said method is regarded merely as an aid in investigation carried on under the superintendence of a science already in existence. It is impossible to get over the fact that in meteorology, medicine, and other physical sciences statistical inquiries are plainly and obviously examples of the employment of a method, like microscopy, spectrum analysis, or the use of the telescope. Why should the fact of their employment in sociology be considered as authorizing the classification of the phenomena thus dealt with to form a new science ?

The most effective argument put forward by the advocates of this view is the assertion that statistics are merely a convenient aid to investigation in the majority of sciences, but are the sole method of inquiry in the case of sociology. Dr Mayr especially (Gesetzmassigkeit, Sze., p. 14 sq.) makes use of this argument, and illustrates it with his usual ability ; but his reasoning is very far from being conclusive. When, indeed, it is tested by reference to the important class of social facts which are named economic, it becomes obvious that the argument breaks down. Economics is a branch - the only scientifically organized branch - of sociology, and statistics are largely used in it, but no one, so far as we are aware, has proposed to call economics a department of statistical science. Sir Rawson W. Rawson, it is true, has boldly proposed to throw over the term "sociology" altogether, - and to describe the study of man in the social state as "statistics," but common usage is too firmly fixed to make this alteration of nomenclature practicable even if it were desirable. The existence of the works of Mr Herbert Spencer and Dr Schaffic alone would render the attempted alteration abortive.

Although, however, the above considerations forbid the acceptance of the Continental opinion that the study of man in the social state is identical with statistics, it must be admitted that without statistics the nature of human society could never become known. For society is an aggregate, or rather a congeries of aggregates. Not only that, but the individuals composing these aggregates are not in juxtaposition, and what is, from the sociological point of view, the same aggregate or organ of the " body politic" is not always composed of the same individuals. Constancy of social form is maintained concurrently with the most extensive changes in the collocation and identity of the particles composing the form. A " nation " is really changed, so far as the individuals composing it are concerned, every moment of time by the operation of the laws of population. But the nation, considered sociologically, remains the same in spite of this slow change in the particles composing it, just as a human being is considered to be the same person year by year, although year by year the particles forming his or her body are constantly being destroyed and fresh particles substituted. Of course the analogy between the life of a human being and the life of a human community must not be pressed too far. Indeed, in several respects human communities more nearly resemble some of the lower forms of animal life than the more highly organized forms of animal existence. There are organisms which are fissiparous, and when cut in two form two fresh independent organisms, so diffused is the vitality of the original organism ; and the same phenomenon may be observed in regard to human communities.

Now the only means whereby the grouping of the individuals forming a social organism can be ascertained, and the changes in the groups year by year observed, is the statistical method. Accordingly the correct view seems to be that it is the function of this method to make perceptible facts regarding the constitution of society on which sociology is to base its conclusions. It is not claimed, or ought not to be claimed, that statistical investigation can supply the whole of the facts a knowledge of which will enable sociologists to form a correct theory of the social life of man. The statistical method is essentially a mathematical procedure, attempting to give a quantitative expression to certain facts ; and the resolution of differences of quality into differences of quantity has not yet been effected even in chemical science. In sociological science the importance of differences of quality is enormous, and the effect of these differences on the conclusions to bo drawn from figures is sometimes neglected, or insufficiently recognized, even by men of unquestionable ability and good faith. The majority of politicians, social "reformers," and amateur handlers of statistics generally are in the habit of drawing the conclusions that seem good to them from such figures as they may obtain, merely by treating as homogeneous quantities which are heterogeneous, and as comparable quantities which are not comparable. Even to the conscientious and intelligent inquirer the difficulty of avoiding mistakes in using statistics prepared by other persons is very great. There are usually " pitfalls" even in the simplest statistical statement, the position and nature of which are known only to the persons who have actually handled what may be called the "raw material" of the statistics in question; and in regard to complex statistical statements the " outsider " cannot be too careful to ascertain from those who compiled them as far as possible what are the points requiring elucidation.

The Statistical iliethod. - This method is a scientific procedure (1) whereby certain phenomena of aggregation not perceptible to the senses are rendered perceptible to the intellect, and (2) furnishing rules for the correct perform ance of the quantitative observation of these phenomena. The class of phenomena of aggregation referred to includes only such phenomena as are too large to be perceptible to the senses. It does not, e.g., include such phenomena as are the subject-matter of microscopy. Things which are very large are often quite as difficult to perceive as those which are very small. A familiar example of this is the difficulty which is sometimes experienced in finding the large names, as of countries or provinces, on a map. Of course the terms "large," "too large," "small," and "too small " must be used with great caution, and with a clear comprehension on the part of the person using them of the standard of measurement implied by the terms in each particular case. A careful study of the first few pages of De Morgan's Diferential and Integral Calculus will materially assist the student of statistics in attaining a grasp of the principles on which standards of measurement should be formed. It is not necessary that he should become acquainted with the calculus itself, or even possess anything more than an elementary knowledge of mathematical science, but it is essential that he should be fully conscious of the fact that " large " and " small " quantities can only be so designated with propriety by reference to a common standard.

Sources whence Statistics are Derivcd. - The term "statistics" in the concrete sense means systematic arrangements of figures representing "primary statistical quantities." A primary statistical quantity is a number obtained from numbers representing phenomena, with a view to enable an observer to perceive a certain other phenomenon related to the former as whole to parts. They represent either a phenomenon of existence at a given point of time or a phenomenon of accretion during a given period. As examples may be mentioned the number of deaths in a given district during a given time, the number of pounds sterling received by the London and North Western Railway during a given time, and the number of "inches of rain " that fell at Greenwich during a given time. Other examples are the number of tons of pig-iron lying in a particular store at a given date, the number of persons residing (the term " residing " to be specially defined) in a given territory at a given date, and the number of pounds sterling representing the private deposits " of the Bank of England at a given date.

Primary Statistical Quantities are the result of labonrs carried on either (A) by Governments or (B) by individuals or public or private corporations.

A. Government Statistics. - (1) A vast mass of statistical material of more or less value comes into existence automatically in modern states in consequence of the ordinary administrative routine of departments. To this class belong the highly important statistical information published in England by the registrar-general, the returns of pauperism issued by the Local Government Board, the reports of inspectors of prisons, factories, schools, and those of sanitary inspectors, as well as the reports of the commissioners of the customs, and the annual statements of trade and navigation prepared by the same officials. There are also the various returns compiled and issued by the Board of Trade, which is the body most nearly resembling the statistical bureaus with which most foreign Governments are furnished. Most of the Government departments publish some statistics for which they are solely responsible as regards both matter and form, and they are very jealous of their right to do so, a fact which is to some extent detrimental to that uniformity as to dates and periods which should bo the ideal of a well-organized system of statistics. Finally may be mentioned the very important set of statistical quantities known as the budget, and the statistics prepared and published by the commissioners of inland revenue, by the post office, and by the national debt commissioners. All these sets of primary statistical quantities arise out of the ordinary work of departments of the public service. Many of them have been in existence, in some form or other, ever since a settled Government existed in the country. There are records of customs receipts at London and other ports of the time of Edward III., covering a period of many years, which leave nothing to be desired in point of precision and uniformity. It may be added that many of these sets of figures are obtained in much the same form by all civilized Governments, and that it is often possible to compare the figures relating to different countries, and thus obtain evidence as to the sociological phenomena of each, but in regard to others there are differences which make comparison difficult.

(2) Besides being responsible for the issue of what may be ealled;administration statistics, all Governments are in the habit of ordering from time to time special inquiries into special subjects