Statistics

  1. Descriptive Statistics: Organizing and Summarizing Data
    1. Tabular and Graphical Presentations
      1. Frequency Distributions
        1. Ungrouped Data
          1. Construction
            1. Frequency Tables
              1. Interpretation
              2. Grouped Data
                1. Class Intervals
                  1. Class Boundaries
                    1. Class Midpoints
                      1. Relative Frequency
                        1. Cumulative Frequency
                      2. Visualizing Categorical Data
                        1. Bar Charts
                          1. Vertical Bar Charts
                            1. Horizontal Bar Charts
                              1. Construction
                                1. Interpretation
                                2. Pie Charts
                                  1. Construction
                                    1. Appropriate Use Cases
                                      1. Interpretation
                                      2. Pareto Charts
                                        1. Construction
                                          1. 80-20 Rule Applications
                                        2. Visualizing Quantitative Data
                                          1. Histograms
                                            1. Construction
                                              1. Choosing Class Width
                                                1. Interpretation
                                                  1. Shape Analysis
                                                  2. Stem-and-Leaf Plots
                                                    1. Construction
                                                      1. Back-to-back Plots
                                                        1. Advantages
                                                        2. Frequency Polygons
                                                          1. Construction
                                                            1. Comparison with Histograms
                                                              1. Smoothing Properties
                                                              2. Ogives (Cumulative Frequency Curves)
                                                                1. Construction
                                                                  1. Uses
                                                                    1. Percentile Reading
                                                                    2. Box-and-Whisker Plots
                                                                      1. Five-Number Summary
                                                                        1. Quartile Calculation
                                                                          1. Identifying Outliers
                                                                            1. Comparative Box Plots
                                                                            2. Scatter Plots
                                                                              1. Bivariate Data Visualization
                                                                                1. Identifying Relationships
                                                                                  1. Pattern Recognition
                                                                              2. Measures of Central Tendency
                                                                                1. Mean
                                                                                  1. Population Mean (μ)
                                                                                    1. Sample Mean (x̄)
                                                                                      1. Calculation Methods
                                                                                        1. Properties of the Mean
                                                                                          1. Sensitivity to Outliers
                                                                                            1. When to Use
                                                                                            2. Median
                                                                                              1. Calculation for Odd and Even Data Sets
                                                                                                1. Position Formula
                                                                                                  1. Robustness to Outliers
                                                                                                    1. When to Use
                                                                                                    2. Mode
                                                                                                      1. Unimodal Distributions
                                                                                                        1. Bimodal Distributions
                                                                                                          1. Multimodal Distributions
                                                                                                            1. Usefulness
                                                                                                              1. Limitations
                                                                                                              2. Weighted Mean
                                                                                                                1. Calculation
                                                                                                                  1. Grade Point Averages
                                                                                                                  2. Choosing Appropriate Measures
                                                                                                                    1. Data Type Considerations
                                                                                                                      1. Distribution Shape Effects
                                                                                                                    2. Measures of Dispersion (Variability)
                                                                                                                      1. Range
                                                                                                                        1. Calculation
                                                                                                                          1. Limitations
                                                                                                                            1. Sensitivity to Outliers
                                                                                                                            2. Interquartile Range (IQR)
                                                                                                                              1. Calculation
                                                                                                                                1. Use in Box Plots
                                                                                                                                  1. Robustness Properties
                                                                                                                                  2. Variance
                                                                                                                                    1. Population Variance (σ²)
                                                                                                                                      1. Sample Variance (s²)
                                                                                                                                        1. Calculation Steps
                                                                                                                                          1. Computational Formulas
                                                                                                                                            1. Units of Measurement
                                                                                                                                            2. Standard Deviation
                                                                                                                                              1. Population Standard Deviation (σ)
                                                                                                                                                1. Sample Standard Deviation (s)
                                                                                                                                                  1. Calculation
                                                                                                                                                    1. Interpretation
                                                                                                                                                      1. Empirical Rule Applications
                                                                                                                                                      2. Coefficient of Variation
                                                                                                                                                        1. Calculation
                                                                                                                                                          1. Comparison Across Data Sets
                                                                                                                                                            1. Relative Variability
                                                                                                                                                              1. When to Use
                                                                                                                                                            2. Measures of Position
                                                                                                                                                              1. Percentiles
                                                                                                                                                                1. Calculation
                                                                                                                                                                  1. Interpretation
                                                                                                                                                                    1. Common Percentiles
                                                                                                                                                                    2. Deciles
                                                                                                                                                                      1. Calculation
                                                                                                                                                                        1. Interpretation
                                                                                                                                                                        2. Quartiles
                                                                                                                                                                          1. First Quartile (Q1)
                                                                                                                                                                            1. Second Quartile (Q2)
                                                                                                                                                                              1. Third Quartile (Q3)
                                                                                                                                                                                1. Calculation
                                                                                                                                                                                  1. Use in Data Analysis
                                                                                                                                                                                  2. Z-scores
                                                                                                                                                                                    1. Calculation
                                                                                                                                                                                      1. Interpretation
                                                                                                                                                                                        1. Standardization of Data
                                                                                                                                                                                          1. Outlier Detection
                                                                                                                                                                                        2. The Shape of a Distribution
                                                                                                                                                                                          1. Skewness
                                                                                                                                                                                            1. Positive Skew
                                                                                                                                                                                              1. Negative Skew
                                                                                                                                                                                                1. Symmetric Distributions
                                                                                                                                                                                                  1. Measurement
                                                                                                                                                                                                    1. Coefficient of Skewness
                                                                                                                                                                                                    2. Kurtosis
                                                                                                                                                                                                      1. Leptokurtic
                                                                                                                                                                                                        1. Mesokurtic
                                                                                                                                                                                                          1. Platykurtic
                                                                                                                                                                                                            1. Interpretation
                                                                                                                                                                                                              1. Coefficient of Kurtosis

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                                                                                                                                                                                                          2. Data Collection and Sampling

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                                                                                                                                                                                                          4. Probability Theory