Schaum´s outline of theory and problems of statistics / Murray R. Spiegel

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Statistics, or statistical methods as it is sometimes called, is playing an increasingly important role in nearly all phases of human endeavour. Formerly dealing only with affairs of the state, thus accounting for its ñame, the influence of statistics has now spread to agriculture, biology, business, chemistry, Communications, economics, education, electronics, medicine, physics, political science, psychology, sociology and numerous other fields of science and engineering. The purpose of this book is to present an introduction to the general statistical principies which will be found useful to all individuáis regardless of their fields of specialization. It has been designed for use either as a supplement to all current standard texts or as a textbook for a formal course in statistics. It should also be of considerable valué as a book of reference for those presently engaged in applications of statistics to their own special problems of research. Each chapter begins with clear statements of pertinent definitions, theorems and principies together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems which in many instances use data drawn from actual statistical situations. The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principies so vital to effective teaching. Numerous derivations of formulae are included among the solved problems. The large number of supple¬mentary problems with answers serve as a complete review of the material of each chapter.The only mathematical background needed for an understanding of the entire book is arithmetic and the elements of algebra. A review of important mathematical concepts used in the book is presented in the first chapter which may either be read at the beginning of the course or referred to later as the need arises. The early part of the book deals with the analysis of frequency distributions and associated measures of central tendency, dispersión, skewness and kurtosis. This leads quite naturally to a discussion of elementary probability theory and applications, which pavés the way for a study of sampling theory. Techniques of large sampling theory, which involve the normal distribution, and applications to statistical estimation and tests of hypotheses and significance are treated first. Small sampling theory, involving Student´s t and the chi-square distributions together with applications, follows in sepárate chapters. A chapter on curve fitting and the method of least squares, which is of interest in itself, leads logically to the topics of correlation and regression involving two variables. Múltiple and partial correlation involving more than two variables are treated in a sepárate chapter. Two final chapters deal with analysis of time series and index numbers respectively.