Schaum's outline of theory and problems of statistics

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Hauptverfasser: Spiegel, Murray R. 1923-1991 (VerfasserIn), Stephens, Larry J. (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: New York [u.a.] McGraw-Hill 2008
Ausgabe:4. ed.
Schriftenreihe:Schaum's outline series
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Datensatz im Suchindex

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adam_text Titel: Schaum s outline of theory and problems of statistics Autor: Spiegel, Murray R. Jahr: 2008 CHAPTER 1 Variables and Graphs 1 Statistics 1 Population and Sample; Inductive and Descriptive Statistics 1 Variables: Discrete and Continuous 1 Rounding of Data 2 Scientific Notation 2 Significant Figures 3 Computations 3 Functions 4 Rectangular Coordinates 4 Graphs 4 Equations 5 Inequalities 5 Logarithms 6 Properties of Logarithms 7 Logarithmic Equations 7 CHAPTER 2 Frequency Distributions 37 Raw Data 37 Arrays 37 Frequency Distributions 37 Class Intervals and Class Limits 38 Class Boundaries 38 The Size, or Width, of a Class Interval 38 The Class Mark 38 General Rules for Forming Frequency Distributions 38 Histograms and Frequency Polygons 39 Relative-Frequency Distributions 39 Cumulative-Frequency Distributions and Ogives 40 Relative Cumulative-Frequency Distributions and Percentage Ogives 40 Frequency Curves and Smoothed Ogives 41 Types of Frequency Curves 41 CHAPTER 3 The Mean, Median, Mode, and Other Measures of Central Tendency 61 Index, or Subscript, Notation 61 Summation Notation 61 Averages, or Measures of Central Tendency 62 xiv CONTENTS The Arithmetic Mean 62 The Weighted Arithmetic Mean 62 Properties of the Arithmetic Mean 63 The Arithmetic Mean Computed from Grouped Data 63 The Median 64 The Mode 64 The Empirical Relation Between the Mean, Median, and Mode 64 The Geometric Mean G 65 The Harmonic Mean H 65 The Relation Between the Arithmetic, Geometric, and Harmonic Means 66 The Root Mean Square 66 Quartiles, Deciles, and Percentiles 66 Software and Measures of Central Tendency 67 CHAPTER 4 The Standard Deviation and Other Measures of Dispersion 95 Dispersion, or Variation 95 The Range 95 The Mean Deviation 95 The Semi-Interquartile Range 96 The 10-90 Percentile Range 96 The Standard Deviation 96 The Variance 97 Short Methods for Computing the Standard Deviation 97 Properties of the Standard Deviation 98 Charlier s Check 99 Sheppard s Correction for Variance 100 Empirical Relations Between Measures of Dispersion 100 Absolute and Relative Dispersion; Coefficient of Variation 100 Standardized Variable; Standard Scores 101 Software and Measures of Dispersion 101 CHAPTER 5 Moments, Skewness, and Kurtosis 123 Moments 123 Moments for Grouped Data 123 Relations Between Moments 124 Computation of Moments for Grouped Data 124 Charlier s Check and Sheppard s Corrections 124 Moments in Dimensionless Form 124 Skewness 125 Kurtosis 125 Population Moments, Skewness, and Kurtosis 126 Software Computation of Skewness and Kurtosis 126 CONTENTS xv CHAPTER 6 Elementary Probability Theory 139 Definitions of Probability 139 Conditional Probability; Independent and Dependent Events 140 Mutually Exclusive Events 141 Probability Distributions 142 Mathematical Expectation 144 Relation Between Population, Sample Mean, and Variance 144 Combinatorial Analysis 145 Combinations 146 Stirling s Approximation to n 146 Relation of Probability to Point Set Theory 146 Euler or Venn Diagrams and Probability 146 CHAPTER 7 The Binomial, Normal, and Poisson Distributions 172 The Binomial Distribution 172 The Normal Distribution 173 Relation Between the Binomial and Normal Distributions 174 The Poisson Distribution 175 Relation Between the Binomial and Poisson Distributions 176 The Multinomial Distribution 177 Fitting Theoretical Distributions to Sample Frequency Distributions , 177 CHAPTER 8 Elementary Sampling Theory 203 Sampling Theory 203 Random Samples and Random Numbers 203 Sampling With and Without Replacement 204 Sampling Distributions 204 Sampling Distribution of Means 204 Sampling Distribution of Proportions 205 Sampling Distributions of Differences and Sums 205 Standard Errors 207 Software Demonstration of Elementary Sampling Theory 207 CHAPTER 9 Statistical Estimation Theory 227 Estimation of Parameters 227 Unbiased Estimates 227 Efficient Estimates 228 Point Estimates and Interval Estimates; Their Reliability 228 Confidence-Interval Estimates of Population Parameters 228 Probable Error 230 xvi CONTENTS CHAPTER 10 Statistical Decision Theory 245 Statistical Decisions 245 Statistical Hypotheses 245 Tests of Hypotheses and Significance, or Decision Rules 246 Type I and Type II Errors 246 Level of Significance 246 Tests Involving Normal Distributions 246 Two-Tailed and One-Tailed Tests 247 Special Tests 248 Operating-Characteristic Curves; the Power of a Test 248 p-Values for Hypotheses Tests 248 Control Charts 249 Tests Involving Sample Differences 249 Tests Involving Binomial Distributions 250 CHAPTER 11 Small Sampling Theory 275 Small Samples 275 Student s t Distribution 275 Confidence Intervals 276 Tests of Hypotheses and Significance 277 The Chi-Square Distribution 277 Confidence Intervals for a 278 Degrees of Freedom 279 The F Distribution 279 CHAPTER 12 The Chi-Square Test 294 Observed and Theoretical Frequencies 294 Definition of x2 294 Significance Tests 295 The Chi-Square Test for Goodness of Fit 295 Contingency Tables 296 Yates Correction for Continuity 297 Simple Formulas for Computing %2 297 Coefficient of Contingency 298 Correlation of Attributes 298 Additive Property of x% 299 CHAPTER 13 Curve Fitting and the Method of Least Squares 316 Relationship Between Variables 316 Curve Fitting 316 Equations of Approximating Curves 317 Freehand Method of Curve Fitting 318 The Straight Line 318 The Method of Least Squares 319 CONTENTS xvii The Least-Squares Line 319 Nonlinear Relationships 320 The Least-Squares Parabola 320 Regression 321 Applications to Time Series 321 Problems Involving More Than Two Variables 321 CHAPTER 14 Correlation Theory 345 Correlation and Regression 345 Linear Correlation 345 Measures of Correlation 346 The Least-Squares Regression Lines 346 Standard Error of Estimate 347 Explained and Unexplained Variation 348 Coefficient of Correlation 348 Remarks Concerning the Correlation Coefficient 349 Product-Moment Formula for the Linear Correlation Coefficient 350 Short Computational Formulas 350 Regression Lines and the Linear Correlation Coefficient 351 Correlation of Time Series 351 Correlation of Attributes 351 Sampling Theory of Correlation 351 Sampling Theory of Regression 352 CHAPTER 15 Multiple and Partial Correlation 382 Multiple Correlation 382 Subscript Notation 382 Regression Equations and Regression Planes 382 Normal Equations for the Least-Squares Regression Plane 383 Regression Planes and Correlation Coefficients 383 Standard Error of Estimate 384 Coefficient of Multiple Correlation 384 Change of Dependent Variable 384 Generalizations to More Than Three Variables 385 Partial Correlation 385 Relationships Between Multiple and Partial Correlation Coefficients 386 Nonlinear Multiple Regression 386 CHAPTER 16 Analysis of Variance 403 The Purpose of Analysis of Variance 403 One-Way Classification, or One-Factor Experiments 403 xviii CONTENTS Total Variation, Variation Within Treatments, and Variation Between Treatments 404 Shortcut Methods for Obtaining Variations 404 Mathematical Model for Analysis of Variance 405 Expected Values of the Variations 405 Distributions of the Variations 406 The F Test for the Null Hypothesis of Equal Means 406 Analysis-of-Variance Tables 406 Modifications for Unequal Numbers of Observations 407 Two-Way Classification, or Two-Factor Experiments 407 Notation for Two-Factor Experiments 408 Variations for Two-Factor Experiments 408 Analysis of Variance for Two-Factor Experiments 409 Two-Factor Experiments with Replication 410 Experimental Design 412 CHAPTER 17 Nonparametric tests 446 Introduction 446 The Sign Test 446 The Mann-Whitney U Test 447 The Kruskal-Wallis H Test 448 The H Test Corrected for Ties 448 The Runs Test for Randomness 449 Further Applications of the Runs Test 450 Spearman s Rank Correlation 450 CHAPTER 18 Statistical Process Control and Process Capability 480 General Discussion of Control Charts 480 Variables and Attributes Control Charts 481 JT-bar and R Charts 481 Tests for Special Causes 484 Process Capability 484 P- and AT-Charts 487 Other Control Charts 489 Answers to Supplementary Problems 505 Appendixes 559 I Ordinates (Y) of the Standard Normal Curve at z 561 II Areas Under the Standard Normal Curve from 0 to z 562 HI Percentile Values (tp) for Student s t Distribution with v Degrees of Freedom 563 IV Percentile Values {%],) for the Chi-Square Distribution with v Degrees of Freedom 564 CONTENTS xix V 95th Percentile Values for the F Distribution 565 VI 99th Percentile Values for the F Distribution 566 VII Four-Place Common Logarithms 567 VIII Values of e~x 569 IX Random Numbers 570 Index 571
adam_txt Titel: Schaum's outline of theory and problems of statistics Autor: Spiegel, Murray R. Jahr: 2008 CHAPTER 1 Variables and Graphs 1 Statistics 1 Population and Sample; Inductive and Descriptive Statistics 1 Variables: Discrete and Continuous 1 Rounding of Data 2 Scientific Notation 2 Significant Figures 3 Computations 3 Functions 4 Rectangular Coordinates 4 Graphs 4 Equations 5 Inequalities 5 Logarithms 6 Properties of Logarithms 7 Logarithmic Equations 7 CHAPTER 2 Frequency Distributions 37 Raw Data 37 Arrays 37 Frequency Distributions 37 Class Intervals and Class Limits 38 Class Boundaries 38 The Size, or Width, of a Class Interval 38 The Class Mark 38 General Rules for Forming Frequency Distributions 38 Histograms and Frequency Polygons 39 Relative-Frequency Distributions 39 Cumulative-Frequency Distributions and Ogives 40 Relative Cumulative-Frequency Distributions and Percentage Ogives 40 Frequency Curves and Smoothed Ogives 41 Types of Frequency Curves 41 CHAPTER 3 The Mean, Median, Mode, and Other Measures of Central Tendency 61 Index, or Subscript, Notation 61 Summation Notation 61 Averages, or Measures of Central Tendency 62 xiv CONTENTS The Arithmetic Mean 62 The Weighted Arithmetic Mean 62 Properties of the Arithmetic Mean 63 The Arithmetic Mean Computed from Grouped Data 63 The Median 64 The Mode 64 The Empirical Relation Between the Mean, Median, and Mode 64 The Geometric Mean G 65 The Harmonic Mean H 65 The Relation Between the Arithmetic, Geometric, and Harmonic Means 66 The Root Mean Square 66 Quartiles, Deciles, and Percentiles 66 Software and Measures of Central Tendency 67 CHAPTER 4 The Standard Deviation and Other Measures of Dispersion 95 Dispersion, or Variation 95 The Range 95 The Mean Deviation 95 The Semi-Interquartile Range 96 The 10-90 Percentile Range 96 The Standard Deviation 96 The Variance 97 Short Methods for Computing the Standard Deviation 97 Properties of the Standard Deviation 98 Charlier's Check 99 Sheppard's Correction for Variance 100 Empirical Relations Between Measures of Dispersion 100 Absolute and Relative Dispersion; Coefficient of Variation 100 Standardized Variable; Standard Scores 101 Software and Measures of Dispersion 101 CHAPTER 5 Moments, Skewness, and Kurtosis 123 Moments 123 Moments for Grouped Data 123 Relations Between Moments 124 Computation of Moments for Grouped Data 124 Charlier's Check and Sheppard's Corrections 124 Moments in Dimensionless Form 124 Skewness 125 Kurtosis 125 Population Moments, Skewness, and Kurtosis 126 Software Computation of Skewness and Kurtosis 126 CONTENTS xv CHAPTER 6 Elementary Probability Theory 139 Definitions of Probability 139 Conditional Probability; Independent and Dependent Events 140 Mutually Exclusive Events 141 Probability Distributions 142 Mathematical Expectation 144 Relation Between Population, Sample Mean, and Variance 144 Combinatorial Analysis 145 Combinations 146 Stirling's Approximation to n\ 146 Relation of Probability to Point Set Theory 146 Euler or Venn Diagrams and Probability 146 CHAPTER 7 The Binomial, Normal, and Poisson Distributions 172 The Binomial Distribution 172 The Normal Distribution 173 Relation Between the Binomial and Normal Distributions 174 The Poisson Distribution 175 Relation Between the Binomial and Poisson Distributions 176 The Multinomial Distribution 177 Fitting Theoretical Distributions to Sample Frequency Distributions , 177 CHAPTER 8 Elementary Sampling Theory 203 Sampling Theory 203 Random Samples and Random Numbers 203 Sampling With and Without Replacement 204 Sampling Distributions 204 Sampling Distribution of Means 204 Sampling Distribution of Proportions 205 Sampling Distributions of Differences and Sums 205 Standard Errors 207 Software Demonstration of Elementary Sampling Theory 207 CHAPTER 9 Statistical Estimation Theory 227 Estimation of Parameters 227 Unbiased Estimates 227 Efficient Estimates 228 Point Estimates and Interval Estimates; Their Reliability 228 Confidence-Interval Estimates of Population Parameters 228 Probable Error 230 xvi CONTENTS CHAPTER 10 Statistical Decision Theory 245 Statistical Decisions 245 Statistical Hypotheses 245 Tests of Hypotheses and Significance, or Decision Rules 246 Type I and Type II Errors 246 Level of Significance 246 Tests Involving Normal Distributions 246 Two-Tailed and One-Tailed Tests 247 Special Tests 248 Operating-Characteristic Curves; the Power of a Test 248 p-Values for Hypotheses Tests 248 Control Charts 249 Tests Involving Sample Differences 249 Tests Involving Binomial Distributions 250 CHAPTER 11 Small Sampling Theory 275 Small Samples 275 Student's t Distribution 275 Confidence Intervals 276 Tests of Hypotheses and Significance 277 The Chi-Square Distribution 277 Confidence Intervals for a 278 Degrees of Freedom 279 The F Distribution " 279 CHAPTER 12 The Chi-Square Test 294 Observed and Theoretical Frequencies 294 Definition of x2 294 Significance Tests 295 The Chi-Square Test for Goodness of Fit 295 Contingency Tables ' 296 Yates' Correction for Continuity 297 Simple Formulas for Computing %2 297 Coefficient of Contingency 298 Correlation of Attributes 298 Additive Property of x% 299 CHAPTER 13 Curve Fitting and the Method of Least Squares 316 Relationship Between Variables 316 Curve Fitting 316 Equations of Approximating Curves 317 Freehand Method of Curve Fitting 318 The Straight Line 318 The Method of Least Squares 319 CONTENTS xvii The Least-Squares Line 319 Nonlinear Relationships 320 The Least-Squares Parabola 320 Regression 321 Applications to Time Series 321 Problems Involving More Than Two Variables 321 CHAPTER 14 Correlation Theory 345 Correlation and Regression 345 Linear Correlation 345 Measures of Correlation 346 The Least-Squares Regression Lines 346 Standard Error of Estimate 347 Explained and Unexplained Variation 348 Coefficient of Correlation 348 Remarks Concerning the Correlation Coefficient 349 Product-Moment Formula for the Linear Correlation Coefficient 350 Short Computational Formulas 350 Regression Lines and the Linear Correlation Coefficient 351 Correlation of Time Series 351 Correlation of Attributes 351 Sampling Theory of Correlation 351 Sampling Theory of Regression 352 CHAPTER 15 Multiple and Partial Correlation 382 Multiple Correlation 382 Subscript Notation 382 Regression Equations and Regression Planes 382 Normal Equations for the Least-Squares Regression Plane 383 Regression Planes and Correlation Coefficients 383 Standard Error of Estimate 384 Coefficient of Multiple Correlation 384 Change of Dependent Variable 384 Generalizations to More Than Three Variables 385 Partial Correlation 385 Relationships Between Multiple and Partial Correlation Coefficients 386 Nonlinear Multiple Regression 386 CHAPTER 16 Analysis of Variance 403 The Purpose of Analysis of Variance 403 One-Way Classification, or One-Factor Experiments 403 xviii CONTENTS Total Variation, Variation Within Treatments, and Variation Between Treatments 404 Shortcut Methods for Obtaining Variations 404 Mathematical Model for Analysis of Variance 405 Expected Values of the Variations 405 Distributions of the Variations 406 The F Test for the Null Hypothesis of Equal Means 406 Analysis-of-Variance Tables 406 Modifications for Unequal Numbers of Observations 407 Two-Way Classification, or Two-Factor Experiments 407 Notation for Two-Factor Experiments 408 Variations for Two-Factor Experiments 408 Analysis of Variance for Two-Factor Experiments 409 Two-Factor Experiments with Replication 410 Experimental Design 412 CHAPTER 17 Nonparametric tests 446 Introduction 446 The Sign Test 446 The Mann-Whitney U Test 447 The Kruskal-Wallis H Test 448 The H Test Corrected for Ties 448 The Runs Test for Randomness 449 Further Applications of the Runs Test 450 Spearman's Rank Correlation 450 CHAPTER 18 Statistical Process Control and Process Capability 480 General Discussion of Control Charts 480 Variables and Attributes Control Charts 481 JT-bar and R Charts 481 Tests for Special Causes 484 Process Capability 484 P- and AT-Charts 487 Other Control Charts 489 Answers to Supplementary Problems 505 Appendixes 559 I Ordinates (Y) of the Standard Normal Curve at z 561 II Areas Under the Standard Normal Curve from 0 to z 562 HI Percentile Values (tp) for Student's t Distribution with v Degrees of Freedom 563 IV Percentile Values {%],) for the Chi-Square Distribution with v Degrees of Freedom 564 CONTENTS xix V 95th Percentile Values for the F Distribution 565 VI 99th Percentile Values for the F Distribution 566 VII Four-Place Common Logarithms 567 VIII Values of e~x 569 IX Random Numbers 570 Index 571
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genre (DE-588)4151278-9 Einführung gnd-content
genre_facet Einführung
id DE-604.BV022449706
illustrated Illustrated
index_date 2024-07-02T17:35:55Z
indexdate 2024-07-09T20:57:50Z
institution BVB
isbn 9780071485845
0071485848
language English
oai_aleph_id oai:aleph.bib-bvb.de:BVB01-015657606
oclc_num 610662699
open_access_boolean
owner DE-355
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DE-1050
owner_facet DE-355
DE-BY-UBR
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physical XIX, 577 S. Ill., graph. Darst.
publishDate 2008
publishDateSearch 2008
publishDateSort 2008
publisher McGraw-Hill
record_format marc
series2 Schaum's outline series
spelling Spiegel, Murray R. 1923-1991 Verfasser (DE-588)109314840 aut
Schaum's outline of theory and problems of statistics Murray R. Spiegel ; Larry J. Stephens
Theory and problems of statistics
Statistics
4. ed.
New York [u.a.] McGraw-Hill 2008
XIX, 577 S. Ill., graph. Darst.
txt rdacontent
n rdamedia
nc rdacarrier
Schaum's outline series
Mathematical statistics Outlines, syllabi, etc
Mathematical statistics Problems, exercises, etc
Statistics as Topic Outlines
Statistics as Topic Problems and Exercises
Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf
Verteilungstheorie (DE-588)4133628-8 gnd rswk-swf
Häufigkeit (DE-588)4259535-6 gnd rswk-swf
Stichprobe (DE-588)4057502-0 gnd rswk-swf
Theorie (DE-588)4059787-8 gnd rswk-swf
Korrelation (DE-588)4165343-9 gnd rswk-swf
Statistik (DE-588)4056995-0 gnd rswk-swf
(DE-588)4151278-9 Einführung gnd-content
Statistik (DE-588)4056995-0 s
Theorie (DE-588)4059787-8 s
DE-604
Wahrscheinlichkeit (DE-588)4137007-7 s
1\p DE-604
Häufigkeit (DE-588)4259535-6 s
2\p DE-604
Stichprobe (DE-588)4057502-0 s
3\p DE-604
Korrelation (DE-588)4165343-9 s
4\p DE-604
Verteilungstheorie (DE-588)4133628-8 s
5\p DE-604
Stephens, Larry J. Verfasser (DE-588)133654826 aut
HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015657606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
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spellingShingle Spiegel, Murray R. 1923-1991
Stephens, Larry J.
Schaum's outline of theory and problems of statistics
Mathematical statistics Outlines, syllabi, etc
Mathematical statistics Problems, exercises, etc
Statistics as Topic Outlines
Statistics as Topic Problems and Exercises
Wahrscheinlichkeit (DE-588)4137007-7 gnd
Verteilungstheorie (DE-588)4133628-8 gnd
Häufigkeit (DE-588)4259535-6 gnd
Stichprobe (DE-588)4057502-0 gnd
Theorie (DE-588)4059787-8 gnd
Korrelation (DE-588)4165343-9 gnd
Statistik (DE-588)4056995-0 gnd
subject_GND (DE-588)4137007-7
(DE-588)4133628-8
(DE-588)4259535-6
(DE-588)4057502-0
(DE-588)4059787-8
(DE-588)4165343-9
(DE-588)4056995-0
(DE-588)4151278-9
title Schaum's outline of theory and problems of statistics
title_alt Theory and problems of statistics
Statistics
title_auth Schaum's outline of theory and problems of statistics
title_exact_search Schaum's outline of theory and problems of statistics
title_exact_search_txtP Schaum's outline of theory and problems of statistics
title_full Schaum's outline of theory and problems of statistics Murray R. Spiegel ; Larry J. Stephens
title_fullStr Schaum's outline of theory and problems of statistics Murray R. Spiegel ; Larry J. Stephens
title_full_unstemmed Schaum's outline of theory and problems of statistics Murray R. Spiegel ; Larry J. Stephens
title_short Schaum's outline of theory and problems of statistics
title_sort schaum s outline of theory and problems of statistics
topic Mathematical statistics Outlines, syllabi, etc
Mathematical statistics Problems, exercises, etc
Statistics as Topic Outlines
Statistics as Topic Problems and Exercises
Wahrscheinlichkeit (DE-588)4137007-7 gnd
Verteilungstheorie (DE-588)4133628-8 gnd
Häufigkeit (DE-588)4259535-6 gnd
Stichprobe (DE-588)4057502-0 gnd
Theorie (DE-588)4059787-8 gnd
Korrelation (DE-588)4165343-9 gnd
Statistik (DE-588)4056995-0 gnd
topic_facet Mathematical statistics Outlines, syllabi, etc
Mathematical statistics Problems, exercises, etc
Statistics as Topic Outlines
Statistics as Topic Problems and Exercises
Wahrscheinlichkeit
Verteilungstheorie
Häufigkeit
Stichprobe
Theorie
Korrelation
Statistik
Einführung
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015657606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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