Quantitative Methods

Quantitative Methods encompass the application of mathematical and statistical techniques to analyze numerical data in order to understand phenomena, test hypotheses, and make predictions. As a cornerstone of both Computer Science and Data Science, these methods are essential for transforming raw data into actionable insights, building predictive models, and evaluating system performance. Key practices include statistical modeling, hypothesis testing, simulation, and the development of machine learning algorithms, all of which rely on rigorous, data-driven approaches to problem-solving.

1. Foundations of Quantitative Analysis
   1. Introduction to Data
      1. Types of Data
         1. Quantitative Data
            1. Discrete Data
               1. Definition and Characteristics
               2. Examples and Applications
               3. Counting vs Measuring
            2. Continuous Data
               1. Definition and Characteristics
               2. Examples and Applications
               3. Measurement Precision
         2. Qualitative Data
            1. Nominal Data
               1. Definition and Characteristics
               2. Examples and Applications
               3. Coding Methods
            2. Ordinal Data
               1. Definition and Characteristics
               2. Examples and Applications
               3. Ranking Properties
      2. Scales of Measurement
         1. Nominal Scale
            1. Properties and Characteristics
            2. Mathematical Operations
            3. Statistical Methods
         2. Ordinal Scale
            1. Properties and Characteristics
            2. Mathematical Operations
            3. Statistical Methods
         3. Interval Scale
            1. Properties and Characteristics
            2. Zero Point Interpretation
            3. Mathematical Operations
            4. Statistical Methods
         4. Ratio Scale
            1. Properties and Characteristics
            2. Absolute Zero
            3. Mathematical Operations
            4. Statistical Methods
      3. Data Collection Methods
         1. Primary Data Collection
            1. Surveys and Questionnaires
               1. Design Principles
               2. Question Types
               3. Response Formats
               4. Sampling Frame
               5. Response Bias
            2. Experiments
               1. Controlled Experiments
               2. Randomized Controlled Trials
               3. Factorial Designs
               4. Control Groups
            3. Observational Studies
               1. Cross-sectional Studies
               2. Longitudinal Studies
               3. Case-control Studies
               4. Cohort Studies
         2. Secondary Data Collection
            1. Administrative Records
            2. Published Statistics
            3. Database Mining
         3. Sampling Methods
            1. Probability Sampling
               1. Simple Random Sampling
               2. Systematic Sampling
               3. Stratified Sampling
               4. Cluster Sampling
            2. Non-probability Sampling
               1. Convenience Sampling
               2. Purposive Sampling
               3. Quota Sampling
      4. Data Quality and Preparation
         1. Data Validation
            1. Accuracy Assessment
            2. Completeness Checks
            3. Consistency Verification
         2. Missing Data
            1. Types of Missing Data
            2. Missing Data Patterns
            3. Imputation Methods
         3. Outlier Detection
            1. Statistical Methods
            2. Graphical Methods
            3. Treatment Options
   2. Descriptive Statistics
      1. Measures of Central Tendency
         1. Arithmetic Mean
            1. Population Mean
            2. Sample Mean
            3. Weighted Mean
            4. Geometric Mean
            5. Harmonic Mean
         2. Median
            1. Calculation for Odd Sample Sizes
            2. Calculation for Even Sample Sizes
            3. Robustness Properties
         3. Mode
            1. Unimodal Distributions
            2. Bimodal Distributions
            3. Multimodal Distributions
            4. No Mode Cases
      2. Measures of Variability
         1. Range
            1. Calculation
            2. Limitations
         2. Variance
            1. Population Variance
            2. Sample Variance
            3. Computational Formulas
         3. Standard Deviation
            1. Population Standard Deviation
            2. Sample Standard Deviation
            3. Interpretation
         4. Interquartile Range
            1. First Quartile
            2. Third Quartile
            3. Calculation Methods
         5. Mean Absolute Deviation
            1. Calculation
            2. Comparison with Standard Deviation
         6. Coefficient of Variation
            1. Calculation
      3. Measures of Position
         1. Percentiles
            1. Calculation Methods
            2. Interpretation
         2. Quartiles
            1. First Quartile
            2. Second Quartile
            3. Third Quartile
            4. Five-Number Summary
         3. Deciles
         4. Z-scores
            1. Standardization Process
            2. Interpretation
      4. Measures of Shape
         1. Skewness
            1. Right Skewness
            2. Left Skewness
            3. Symmetry
            4. Measurement Methods
         2. Kurtosis
            1. Leptokurtic Distributions
            2. Platykurtic Distributions
            3. Mesokurtic Distributions
            4. Excess Kurtosis
      5. Data Visualization
         1. Univariate Displays
            1. Histograms
               1. Construction Rules
               2. Bin Selection
               3. Interpretation
            2. Frequency Polygons
            3. Stem-and-Leaf Plots
            4. Box Plots
               1. Construction
               2. Outlier Identification
               3. Comparative Box Plots
            5. Dot Plots
         2. Categorical Data Displays
            1. Bar Charts
               1. Vertical Bar Charts
               2. Horizontal Bar Charts
               3. Grouped Bar Charts
               4. Stacked Bar Charts
            2. Pie Charts
               1. Construction Guidelines
               2. Limitations
            3. Pareto Charts
         3. Bivariate Displays
            1. Scatter Plots
               1. Construction
               2. Pattern Recognition
               3. Correlation Assessment
            2. Line Graphs
            3. Contingency Tables
   3. Probability Theory
      1. Fundamental Concepts
         1. Random Experiments
            1. Characteristics
         2. Sample Space
            1. Finite Sample Spaces
            2. Infinite Sample Spaces
         3. Events
            1. Simple Events
            2. Compound Events
            3. Complementary Events
            4. Mutually Exclusive Events
         4. Probability Definition
            1. Classical Approach
            2. Relative Frequency Approach
            3. Subjective Approach
      2. Probability Axioms and Properties
         1. Axioms of Probability
            1. Non-negativity
            2. Normalization
            3. Additivity
         2. Basic Properties
            1. Complement Rule
            2. Addition Rule
            3. Multiplication Rule
      3. Conditional Probability
         1. Calculation Methods
         2. Independence
            1. Testing Independence
         3. Bayes' Theorem
            1. Statement
            2. Prior and Posterior Probabilities
      4. Random Variables
         1. Definition and Types
            1. Discrete Random Variables
            2. Continuous Random Variables
         2. Probability Distributions
            1. Probability Mass Function
            2. Probability Density Function
            3. Cumulative Distribution Function
         3. Expected Value
            1. Calculation Methods
         4. Variance and Standard Deviation
            1. Calculation Methods
      5. Common Discrete Distributions
         1. Bernoulli Distribution
            1. Parameters
            2. Mean and Variance
         2. Binomial Distribution
            1. Parameters
            2. Mean and Variance
         3. Poisson Distribution
            1. Parameters
            2. Mean and Variance
         4. Geometric Distribution
            1. Parameters
            2. Mean and Variance
         5. Hypergeometric Distribution
            1. Parameters
            2. Mean and Variance
      6. Common Continuous Distributions
         1. Uniform Distribution
            1. Parameters
            2. Mean and Variance
         2. Normal Distribution
            1. Parameters
            2. Standard Normal Distribution
            3. Empirical Rule
         3. Exponential Distribution
            1. Parameters
            2. Mean and Variance
            3. Memoryless Property
         4. Gamma Distribution
            1. Parameters
            2. Relationship to Exponential
         5. Beta Distribution
            1. Parameters