Fundamentals of Statistics

Preface1. Introduction 2. The Collection, Organization and Representation of Numerical Data 2.1. The Collection of Data 2.2. The Classification of Data 2.3. Graphical Representation of Data 2.4. Random Sampling 2.5. Random Numbers 2.6. How to Use Random Sampling Numbers3. Elementary Probability 3.1. Introduction 3.2. Mutually Exclusive Events 3.3. Independent Events 3.4. Introduction to Permutations and Combinations 3.5. Probability Distributions 3.6. Mathematical Expectation and Arithmetic Mean4. The Binomial and Poisson Distributions 4.1. The Binomial Distribution 4.2. The Mean of the Binomial Distribution 4.3. The Poisson Distribution 4.4. The Mean of the Poisson Distribution 4.5. The Additive Property of the Poisson Distribution5. Measures of Central Tendency 5.1. Introduction 5.2. The Mean 5.3. The Median 5.4. The Mode 5.5. The Geometric Mean6 Measures of Dispersion 6.1. Introduction 6.2. The Range 6.3. The Mean Deviation 6.4. The Variance 6.5. The Coefficient of Variation7 Continuous Distributions 7.1. Introduction 7.2. The Modal and Median Values 7.3. Mathematical Expectation, the Mean and the Variance 7.4. The Mean Deviation about the Mean 7.5. The Rectangular Distribution 8 The Normal Distribution 8.1. Introduction 8.2. Properties of the Normal (or Gaussian) Distribution 8.3. Use of Normal Tables 8.4. Practical Problems 8.5. The Use of the Standardized Variate to Compare the Relative Merits of Variates from Different Normal Distributions 8.6. Arithmetical Probability Graph Paper 8.7. The Normal Approximation to the Binomial Distribution 8.8. The Normal Approximation to the Poisson Distribution 9 Significance Testing and Confidence Intervals 9.1. Introduction 9.2. Tests of a Sample Mean 9.3. Difference of Two Population Means 9.4. Test for Paired Data 9.5. Test for a Population Mean given a Large Sample (Population Variance Unknown) 9.6. Tests for the Difference Between Two Population Means given Two Large Samples (Population Variances Unknown) 9.7. Tests for Population Means given Small Samples (Population Variances Unknown) 9.8. Tests for the Difference Between Two Population Means given Two Small Samples (Population Variances Unknown) 9.9. An Approximate Method for Testing if Two Samples Come from Populations with Equal Means (Sample Sizes Small and Equal) 9.10. Test for Paired Data given Small Samples (Population Variances Unknown) 9.11. Comparison of More Than Two Means 9.12. Confidence Limits10. Quality Control 10.1. Introduction 10.2. Control Charts for Sample Means 10.3. Control Charts for Ranges 10.4. Control Charts for Fraction Defective 10.5. Allowable Width of Control Limits when Tolerance Limits are Specified11. Chi-Squared Distribution 11.1. Introduction 11.2. Definition 11.3. Use of Tables 11.4. Test for Variance 11.5. Additive Property of χ2 11.6. Confidence Intervals for χ2 11.7. Observed and Theoretical Frequencies 11.8. Test for the Binomial Distribution using χ2 11.9. Test for the Poisson Distribution using χ2 11.10. Test for Normality using χ2 11.11. Contingency Tables 11.12. Yates Correction12. The F Distribution (Variance Ratio) 12.1. Introduction 12.2. Definition 12.3. Testing for the Equality of Two Population Variances 12.4. Confidence Limits for the Variance Ratio σ21