Fundamentals of Statistics

Fundamentals of Statistics covers topics on the introduction, fundamentals, and science of statistics. The book discusses the collection, organization and representation of numerical data; elementary probability; the binomial Poisson distributions; and the measures of central tendency. The text describes measures of dispersion for measuring the spread of a distribution; continuous distributions for measuring on a continuous scale; the properties and use of normal distribution; and tests involving the normal or student's ‘t’ distributions. The use of control charts for sample means; the ranges and fraction defective; the chi-squared distribution; the F distribution; and the bivariate distributions are also considered. The book deals with the idea of mathematical expectation and its relationship with mean, variance, and covariance, as well as weighted averages, death rates, and time series. Students studying for advanced level education or higher national certificates in Mechanical or Electrical Engineering, Mathematics, Chemistry, Biology, or Pharmacy, as well as university students taking such courses will find the book invaluable.

Preface

1. 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 Numbers

3. 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 Mean

4. 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 Distribution

5. Measures of Central Tendency

5.1. Introduction

5.2. The Mean

5.3. The Median

5.4. The Mode

5.5. The Geometric Mean

6 Measures of Dispersion

6.1. Introduction

6.2. The Range

6.3. The Mean Deviation

6.4. The Variance

6.5. The Coefficient of Variation

7 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 Limits

10. 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 Specified

11. 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 Correction

12. 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|σ22

13. Bivariate Distributions

13.1. Introduction

13.2. Confidence Intervals for β1 and β0

13.3. Correlation

13.4. Grouped Data

13.5. Rank Correlation

13.6. Ranking of Equal Variates

13.7. Kendall's Coefficient of Rank Correlation (rκ)

14. Mathematical Expectation, Variance and Covariance

14.1. Introduction

14.2. Variance

14.3. Covariance

14.4. Expectation and Variance of the Sum and Difference of Two Variates

15. Weighted Averages, Death Rates and Time Series

15.1. Weighted Averages

15.2. Index Numbers

15.3. Crude and Standardized Death Rates

15.4. Introduction to Time Series

15.5. Moving Averages

15.6. Analysis of a Time Series

Appendix

Solutions

Index