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Basic Business Statistics DCOVA Framework To minimize errors, you use a framework that organizes the set of tasks that you follow to apply statistics properly. The five tasks that comprise the DCOVA framework are: D efine the data that you want to study to solve a problem or meet an objective. C ollect the data from appropriate sources. O rganize the data collected, by developing tables. V isualize the data collected, by developing charts. A nalyze the data collected, to reach conclusions and present those results. You must always do the D efine and C ollect tasks before doing the other three. The order of the other three varies and sometimes all three are done concurrently. In this book, you will learn more about the D efine and C ollect tasks in Chapter 1 and then be introduced to the O rganize and V isualize tasks in Chapter 2. Beginning with Chapter 3, you will learn methods that help complete the A nalyze task. 1 Defining and Collecting Data 16 ( D efine & C ollect) 2 Organizing and Visualizing Variables 41 ( O rganize & V isualize) 3 Numerical Descriptive Measures 120 ( A nalyze from hereafter) 4 Basic Probability 168 5 Discrete Probability Distributions 199 6 The Normal Distribution and Other Continuous Distributions 223 7 Sampling Distributions 252 8 Confidence Interval Estimation 275 9 Fundamentals of Hypothesis Testing: One-Sample Tests 311 10 Two-Sample Tests 351 11 Analysis of Variance 398 12 Chi-Square and Nonparametric Tests 440 13 Simple Linear Regression 484 14 Introduction to Multiple Regression 536 15 Multiple Regression Model Building 592 16 Time-Series Forecasting 629 17 Business Analytics 678 18 Getting Ready to Analyze Data in the Future 704 19 Statistical Applications in Quality Management ( online ) 19-1 20 Decision Making ( online ) 20-1 1 Defining and Collecting Data 16 1.1 Defining Variables 17 Classifying Variables by Type 17 Measurement Scales 18 1.2 Collecting Data 19 Populations and Samples 20 Data Sources 20
1.3 Types of Sampling Methods 21 Simple Random Sample 22 Systematic Sample 22 Stratified Sample 23 Cluster Sample 23 1.4 Data Cleaning 24 Invalid Variable Values 25 Coding Errors 25 Data Integration Errors 25 Missing Values 26 Algorithmic Cleaning of Extreme Numerical Values 26 1.5 Other Data Preprocessing Tasks 26 Data Formatting 26 Stacking and Unstacking Data 27 Recoding Variables 27 1.6 Types of Survey Errors 28 Coverage Error 28 Nonresponse Error 28 Sampling Error 28 Measurement Error 29 Ethical Issues About Surveys 29 2 Organizing and Visualizing Variables 41 2.1 Organizing Categorical Variables 42 The Summary Table 42 The Contingency Table 43 2.2 Organizing Numerical Variables 46 The Frequency Distribution 47 Classes and Excel Bins 49 The Relative Frequency Distribution and the Percentage Distribution 49 The Cumulative Distribution 51 2.3 Visualizing Categorical Variables 54 The Bar Chart 54 The Pie Chart and the Doughnut Chart 55 The Pareto Chart 56 Visualizing Two Categorical Variables 58 2.4 Visualizing Numerical Variables 61 The Stem-and-Leaf Display 61 The Histogram 61 The Percentage Polygon 63 The Cumulative Percentage Polygon (Ogive) 64 2.5 Visualizing Two Numerical Variables 67 The Scatter Plot 67 The Time-Series Plot 68 2.6 Organizing a Mix of Variables 70 Drill-down 71 2.7 Visualizing a Mix of Variables 72 Colored Scatter Plot 72 Bubble Charts 73 PivotChart (Excel) 73 Treemap (Excel, JMP) 73 Sparklines (Excel) 74 2.8 Filtering and Querying Data 75 Excel Slicers 75 2.9 Pitfalls in Organizing and Visualizing Variables 77 Obscuring Data 77
Creating False 3 Numerical Descriptive Measures 120 3.1 Measures of Central Tendency 121 The Mean 121 The Median 123 The Mode 124 The Geometric Mean 125 3.2 Measures of Variation and Shape 126 The Range 126 The Variance and the Standard Deviation 127 The Coefficient of Variation 130 Z Scores 130 Shape: Skewness 132 Shape: Kurtosis 132 3.3 Exploring Numerical Variables 137 Quartiles 137 EXHIBIT: Rules for Calculating the Quartiles from a Set of Ranked Values 137 The Interquartile Range 139 The Five-Number Summary 139 The Boxplot 141 3.4 Numerical Descriptive Measures for a Population 143 The Population Mean 144 The Population Variance and Standard Deviation 144 The Empirical Rule 145 Chebyshev's Theorem 146 3.5 The Covariance and the Coefficient of Correlation 148 The Covariance 148 The Coefficient of Correlation 148 3.6 Descriptive Statistics: Pitfalls and Ethical Issues 152 The greater the spread or dispersion of the data, the larger the range, variance, and standard deviation. The smaller the spread or dispersion of the data, the smaller the range, variance, and standard deviation. If the values are all the same (no variation in the data), the range, variance, and standard deviation will all equal zero. Measures of variation (the range, variance, and standard deviation) are never negative. You constructed boxplots to visualize the distribution of the data. You also learned how the coefficient of correlation describes the relationship between two numerical variables. Type of Analysis Methods Central tendency Mean, median, mode Variation and shape Quartiles, range, interquartile range, variance, standard deviation, coefficient of variation, Z scores, skewness,
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