I Introduction to Statistics 1 1.1 Introduction 1 What Is Statistics? 1 1.2 Why Sample? 8 Why Sample? 8 1.3 Sampling Techniques 10 Random or Probability Sampling Techniques 11 1.4 Uses of Statistics 16 1.5 Misuses of Statistics 18 Misleading Graphs 18 Non-Representative Samples 20 Inappropriate Comparisons 21 The Omission of Variation About an Average 21 1.6 Overview and Summary 21 ¿ 2 Organizing and Presenting Data 31 2.1 Introduction 31 2.2 Classifications of Data 33 Categorical and Numerical Variables 34 Continuous and Discrete Data 34 2.3 Exploring Data Using the Stem-and-Leaf Display 36 Back-to-Back Stem-and-Leaf Display 40 2.4 Frequency Distribution Tables 41 Frequency Distribution Table for Categorical Data 41 Frequency Distribution Table for Numerical Data 42 Relative Frequency Distributions 47 Cumulative Frequency Distributions 49 2.5 Graphs: Bar Graph, Histogram, Frequency Polygon and Ogive 52 Bar Graph 52 Histogram 54 Frequency Polygon and Ogive 61 2.6 Specialty Graphs: Pie Chart and Pictograph 65 2.7 Identifying Shapes and Interpreting Graphs 66 Shapes of Distributions 66 Interpreting Graphs 69 2.8 Using Technology 71 Graphing Calculator Display of a Histogram, Frequency Polygon and Ogive 73 ¿ 3 Numerical Techniques for Describing Data 85 3.1 Measures of Central Tendency 86 The Mean 86 Sample Mean 87 Population Mean 88 Other Calculations Using Σ 89 The Median 92 The Mode 95 The Relationship of the Mean, Median and Mode 98 The Mode and Its Location within the Distribution Shapes 99 The Median and Its Location within the Distribution Shapes 99 The Mean and Its Location within the Distribution Shapes 99 Symmetric Bell-Shaped Distribution 99 Skewed to the Left Distribution 100 Skewed to the Right Distribution 100 Comparing the Mean, the Median and the Mode 101 3.2 Measures of Variability 103 The Range 103 The Variance and Standard Deviation of a Sample 105 Interpretation of the Standard Deviation 108 The Variance and Standard Deviation of a Population 110 Using the Sample Standard Deviation to Estimate the Population Standard Deviation 114 3.3 Applications of the Standard Deviation 115 Chebyshev''s Theorem 115 Empirical Rule 117 Using the Range to Obtain an Estimate of the Standard Deviation 118 3.4 Measures of Relative Standing 122 z Score 123 Detecting Outliers Using z Scores 126 Converting z Scores to Raw Scores 126 Percentile Rank and Percentiles 128 Deciles and Quartiles 130 3.5 Box-and-Whisker Plot: An Exploratory Data Analysis Technique 133 3.6 Using Technology 143 ¿ 4 Linear Correlation and Regression Analysis 169 4.1 Introduction 169 4.2 The Scatter Diagram 170 4.3 The Coefficient of Linear Correlation 177 Some Cautions Regarding the Interpretation of Correlation Results 181 4.4 More on the Relationship Between the Correlation Coefficient and the Scatter Diagram 181 4.5 The Coefficient of Determination 182 4.6 Linear Regression Analysis 183 Interpolation versus Extrapolation 188 Regression Analysis Concept Revisited 190 4.7 Using Technology 193 ¿ 5 Probability 205 5.1 Introduction 205 The Birthday Problem 205 Chance! Chance! Chance! 206 5.2 Some Terms Used in Probability 206 Using a Tree Diagram to Construct a Sample Space 208 5.3 Permutations and Combinations 213 Permutation 213 Combination 219 Methods of Selection 223 Explaining the Difference Between the Idea of a Permutation and a Combination 224 5.4 Probability 225 Alternate Approaches to Assigning a Probability 226 Another Approach to Defining Probability 231 Relative Frequency Concept of Probability or Posteriori Probability 231 Another Approach to Defining Probability 233 Subjective or Personal