Manual The Britannica Guide to Statistics and Probability (Math Explained)

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Bitmap technology, together with high-resolution display screens and the development of graphics standards that make software less machine-dependent, has led to the explosive growth of the field. Support for all these activities evolved into the field of computer science known as graphics and visual computing. Closely related to this field is the design and analysis of systems that interact directly with users who are carrying out various computational tasks.

GUI design, which was pioneered by Xerox and was later picked up by Apple Macintosh and finally by Microsoft Windows , is important because it constitutes what people see and do when they interact with a computing device. The design of appropriate user interfaces for all types of users has evolved into the computer science field known as human-computer interaction HCI. The field of computer architecture and organization has also evolved dramatically since the first stored-program computers were developed in the s.

So called time-sharing systems emerged in the s to allow several users to run programs at the same time from different terminals that were hard-wired to the computer.

The s saw the development of the first wide-area computer networks WANs and protocols for transferring information at high speeds between computers separated by large distances. As these activities evolved, they coalesced into the computer science field called networking and communications.

A major accomplishment of this field was the development of the Internet. These discoveries were the origin of the computer science field known as algorithms and complexity. A key part of this field is the study and application of data structures that are appropriate to different applications. Data structures, along with the development of optimal algorithms for inserting, deleting, and locating data in such structures, are a major concern of computer scientists because they are so heavily used in computer software, most notably in compilers, operating systems, file systems, and search engines.

In the s the invention of magnetic disk storage provided rapid access to data located at an arbitrary place on the disk.

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This invention led not only to more cleverly designed file systems but also to the development of database and information retrieval systems, which later became essential for storing, retrieving, and transmitting large amounts and wide varieties of data across the Internet. This field of computer science is known as information management. Another long-term goal of computer science research is the creation of computing machines and robotic devices that can carry out tasks that are typically thought of as requiring human intelligence.

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Such tasks include moving, seeing, hearing, speaking, understanding natural language, thinking, and even exhibiting human emotions. The computer science field of intelligent systems, originally known as artificial intelligence AI , actually predates the first electronic computers in the s, although the term artificial intelligence was not coined until Three developments in computing in the early part of the 21st century—mobile computing, client-server computing , and computer hacking—contributed to the emergence of three new fields in computer science: platform-based development, parallel and distributed computing , and security and information assurance.

Platform-based development is the study of the special needs of mobile devices, their operating systems, and their applications.

Parallel and distributed computing concerns the development of architectures and programming languages that support the development of algorithms whose components can run simultaneously and asynchronously rather than sequentially , in order to make better use of time and space.

Security and information assurance deals with the design of computing systems and software that protects the integrity and security of data, as well as the privacy of individuals who are characterized by that data. Finally, a particular concern of computer science throughout its history is the unique societal impact that accompanies computer science research and technological advancements.

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View Larger Images. The Britannica Guide to Statistics and Probability. Price : Rs. Delivered in business days through India Post as Register Parcel. 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 er 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 be 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 " pit-falls " 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 Method. 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. 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 caste.

A careful study of the first few pages of De Morgan's Differential 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.

It is also necessary that he should be acquainted with the theory of probability as applied to statistical investigations, the need of which is well set forth by Mr A. Bowley in Part II. Valuable instruction on this technical subject can be obtained from monographs by Professor F. Sources whence Statistics are Derived. They represent either a phenomenon of existence at a given point of time or a phenomenon of accretion during a given period. 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 labours carried on either A by governments or B by individuals or public or private corporations. A Government Statistics. 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.

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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 be 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. 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.

Besides being responsible for the issue of what may be called administration statistics, all governments are in the habit of ordering from time to time special inquiries into special subjects of interest, either to obtain additional information needful for administrative purposes, or, in countries possessed of representative institutions, to supply statistics asked for by parliaments or congresses.

It is not necessary to refer particularly to this class of statistical information, except in the case of the census. This is an inquiry of such great importance that it may be regarded as one of the regular administrative duties of governments, though as the census is only taken once in a series of years it must be mentioned under the head of occasional or special inquiries undertaken by governments.

In the United Kingdom the work is done by the registrars-general who are in office when the period for taking the census comes round.

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On the Continent the work is carried out by the statistical bureaus of each country - except France, where it is under the supervision of the minister of the interior. The new regulations as to income-tax assessment and the new land taxes will furnish the government with much fresh information as to incomes; and the census of production ordered in the session of and already carried out as regards a number of trades will also be useful. The primary statistical quantities for which individuals or corporations are responsible may be divided into three categories: t.

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Among those which are compiled in obedience to the law of the land are the accounts furnished by municipal corporations, by the Bank of England, by railway, gas, water, banking, insurance and other public companies making returns to the board of trade, by trades unions, and by other bodies which are obliged to make returns to the registrar of friendly societies. The information thus obtained is published in full by the departments receiving it, and is also furnished by the companies themselves to their proprietors or members.

An enormous mass of statistical information is furnished xxv. With these statistics may be classed the figures furnished by the various trade associations, some of them of great importance, such as Lloyd's, the London Stock Exchange, the British Iron Trade Association, the London Corn Exchange, the Institute of Bankers, the Institute of Actuaries, and other such bodies too numerous to mention.

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There are cases in which individuals have devoted themselves with more or less success to obtaining original statistics on special points. The great work done by Messrs Behm and Wagner in arriving at an approximate estimate of the population of the earth does not belong to this category, though its results are really primary statistical quantities. Many of these results have not been arrived at by a direct process of enumeration at all, but by ingenious processes of inference. It need hardly be said that it is not easy for individuals to obtain the materials for any primary statistical quantity of importance, but it has been done in some cases with success.

The investigations of Mr Charles Booth into labour and wages questions, carried out with care over many years, are a remarkable example of this. Operations Performed on Primary Statistical Quantities. In order to form statistics properly so called the primary statistical quantities must be formed into tables, and in the formation of these tables lies the art of the statistician.

It is not a very difficult art when the principles relating to it have been properly grasped, but those who are unfamiliar with the subject are apt to underrate the difficulty of correctly practising it. Simple Tables.

The Britannica Guide to Statistics and Probability (Math Explained)

This is a matter which is often neglected, and it is a source of much waste of time and occasionally of misapprehension to those who have to, study the figures thus presented. No table ought to be considered complete without a " heading " accurately describing its contents, and it is frequently necessary that such headings should be rather long. It has been said that " you can prove anything by statistics. If this popular saying ran " you can prove anything by tables with slovenly and ambiguous headings," it might be assented to without hesitation. The false " statistical " facts which obtain a hold of the public mind may often be traced to some widely circulated table, to which, either from stupidity or carelessness, an erroneous or inaccurate " heading " has been affixed.

A statistical table in its simplest form consists of " primaries " representing phenomena of the same class, but existing at different points of time, or coming into existence during different portions of time. This is all that is essential to a table, though other things are usually added to it as an aid to its comprehension. A table stating the number of persons residing in each county of England on a given day of a given year, and also, in another column, the corresponding numbers for the same counties on the corresponding day of the tenth year subsequently, would be a simple tabular statement of the general facts regarding the total population of those counties supplied by two successive censuses.

Various figures might, however, be added to it which would greatly add to its clearness.