Lecture Notes: Data Science Statistics Basics

Topics Covered

1. Introduction to Data Science Statistics

   • Differences between Descriptive and Inferential Statistics

2. Descriptive Statistics Topics

   • Measure of Central Tendency
   • Measure of Dispersions
   • Data Summarizing Tools
     • Histograms
     • Box Plot
     • Whisker Plot

3. Detailed Breakdown of Descriptive Statistics

   • Histograms: Understanding PDF, CDF, and creation techniques.
   • Probability & Permutations:
     • Importance in Data Science
     • Mean, Median, Mode
     • Variance, Standard Deviation
   • Distributions:
     • Gaussian (Normal)
     • Log-Normal
     • Binomial
     • Bernoulli
     • Pareto (Power Law)
     • Standard Normal

4. Techniques in Standard Normal Distribution

   • Transformation
   • Standardization
   • QQ Plot
   • Determining Normality of a Distribution

5. Inferential Statistics

   • Hypothesis Testing: Null and Alternative Hypotheses
     • P-Values
     • Confidence Intervals
     • Z-Test, T-Test, Chi-Square Test
     • ANOVA (F-Test)
   • Importance of Hypothesis Testing
     • Defining P-Value and Z, T tables

6. Introduction to Statistics

   • Definitions: Collection, Organization, and Analysis of Data
   • Importance in Decision Making
   • Data: Facts/Information that can be Measured

7. Types of Statistics: Descriptive vs. Inferential

   • Descriptive Statistics: Organizing and Summarizing Data
     • Example: Average age of students
   • Inferential Statistics: Making Conclusions from Data
     • Example: IQ of class vs. college

8. Population and Sample Concepts

   • Population: Complete data set
   • Sample: Subset of the population
   • Sampling Techniques
     • Simple Random Sampling
     • Stratified Sampling
     • Systematic Sampling
     • Convenience Sampling

9. Variables

   • Types
     • Quantitative: Can be measured numerically (e.g., Age, Height, Weight)
     • Qualitative (Categorical): Based on characteristics (e.g., Gender, Blood Group)
   • Quantitative Variables
     • Discrete: Whole numbers (e.g., Number of Bank Accounts)
     • Continuous: Any value (e.g., Height, Weight)

10. Variable Measurement Levels

    • Nominal: Categorical (e.g., Color, Gender)
    • Ordinal: Rank-Ordered (e.g., Ranks)
    • Interval: Order Matters, No Natural Zero (e.g., Temperature in Fahrenheit)
    • Ratio: Interval with a Natural Zero (e.g., Height, Weight)

11. Frequency Distribution

    • Organizing data into a frequency table
    • Cumulative Frequency
      • Example: Counting flowers types

12. **Bar Graph vs. Histogram

    • Bar Graph: Discrete variables
    • Histogram: Continuous variables

13. Probability and Sampling Techniques

    • Determining the likelihood of events
    • Various Sampling Techniques
      • Simple Random Sampling
      • Stratified Sampling
      • Systematic Sampling
      • Convenience Sampling

14. Central Measure of Tendency: Mean, Median, Mode

    • How to compute and their significance in presence of outliers
    • When to use each measure

15. Measure of Dispersion: Variance and Standard Deviation

    • Concept and importance of spread
    • Calculations involving Population and Sample variance

16. Percentiles and Quartiles for Outlier Detection

    • Examples of outlier detection
    • Calculation of Percentiles, Interquartile Range (IQR), and Fences

17. Hypothesis Testing and Types of Errors

    • Type 1 and Type 2 Errors
    • One-Tailed and Two-Tailed Tests

18. Confusion Matrix

    • True Positive, True Negative, False Positive, False Negative

19. Distributions and Tests with Examples

    • Binomial, Bernoulli, Poisson Behavior, and more
    • Central Limit Theorem
    • Practical examples and calculations
    • Z Test, T Test, Chi-Square Test, and ANOVA Test

20. Covariance and Correlation

    • Definitions and formulas
    • Real-world examples
    • Calculating covariance and correlation using Python

21. Tools and Implementations in Python

    • Google Collab for Z Test, T Test, Chi-Square Test
    • Libraries: Pandas, Seaborn, Numpy**

Notes and Observations

• Important Definitions and Formulas: Keep track of essential formulas, definitions, and their practical usage.
• Statistical Tests: Understand the context and when to use which type of tests (Z, T, Chi-Square, ANOVA).
• Visualization Techniques: Learn different methods to visualize data like histograms, bar charts, box plots, QQ plots, etc.
• Practical Coding Examples: Practicing code is essential to understand distributions, tests, and transformations.
• Outlier Analysis: Important techniques for detecting and handling outliers using IQR and Standard Deviation.
• Sampling Techniques: Understand types of sampling methods for better data collection.