How Much Math You Need to Learn to Become a Data Professional

Jul 16, 2024

How Much Math You Need to Learn to Become a Data Professional - Lecture Transcript Notes

Introduction

  • Presenter: Sum Shukla
  • Purpose: Understand necessary math topics for becoming a data professional
  • Note: Free master class available on the Scaler event page by industry experts.
  • Subscription reminder for Scaler's YouTube channel.

Data Professional Roles

  • Data Analyst: Entry point; interacts with data; first contact for data requirements.
  • Business Analyst: Extracts insights from data to solve business problems; requires business knowledge.
  • Data Scientist: Uses data to create complex models and algorithms for predictions and optimizations.
  • Other Roles: MLOps Engineer, Data Engineer, ML Manager, AI Manager, etc.

Importance of Math in Data Professions

  • Myth: Can become a data professional without math, just with Python, SQL, and ML algorithms.
  • Reality: Math is essential; all ML algorithms are based on mathematical models.
  • Core Math Topics:
    1. Statistics
    2. Linear Algebra
    3. Calculus
    4. Discrete Mathematics

Statistics

Subtopics:

  1. Descriptive Statistics:
    • Measures of Central Tendency (Mean, Median, Mode)
    • Measures of Dispersion (Variance, Standard Deviation)
  2. Inferential Statistics
  3. Hypothesis Testing
  4. Regression
  5. Time Series Analysis

Descriptive Statistics Detailed Concepts:

  • Measures of Central Tendency: Mean, Median, Mode
  • Measures of Dispersion: Variance and Standard Deviation

Example Explanation:

  • Mean: Sum of all observations divided by the number of observations.
  • Median: The middle value that divides the dataset into two halves.
  • Mode: The value that appears most frequently.
  • Variance: Measures the spread of data points from the mean.
  • Standard Deviation: Square root of variance, indicates how spread out the data is.

Linear Algebra

Subtopics:

  1. Matrices:
    • Definition and structure (rows, columns)
    • Shape determination (e.g. 3x3 matrix)
  2. Matrix Operations:
    • Multiplication rules
    • Example calculations
  3. Linear Equations
  4. Optimization

Example Explanation:

  • Matrix Multiplication: Defined rules, operations (e.g., multiplying 3x2 and 2x3 matrices)

Calculus

Subtopics:

  1. Differentiation
  2. Integration
  3. Optimization Techniques

Example Explanation:

  • Differentiation: Slope of a function (example calculation with polynomial function)
  • Partial Differentiation
  • Optimization: Used in neural networks and machine learning models.

Discrete Mathematics

Subtopics:

  1. Combinatorics: Permutation and Combination
  2. Graph Theory
  3. Probability Theory
  4. Set Theory

Example Explanation:

  • Combinations: Number of ways to choose a sample (formula: nCr)
  • Permutations: Number of ways to arrange items (formula: nPr)

Statistics and Probability Course Introduction

Classification of Statistics:

  1. Descriptive Statistics
  2. Inferential Statistics
  3. Hypothesis Testing

Example Explanation:

  • Descriptive: Summarizes data (e.g., mean, median, mode)
  • Inferential: Uses sample data to make generalizations about a population
  • Hypothesis Testing: Tests assumptions (e.g., Dettol kills 99.9% germs claim)

Types of Variables

Classification:

  1. Qualitative:
    • Nominal: No inherent order (e.g., city names)
    • Ordinal: Ordered categories (e.g., grades)
  2. Quantitative:
    • Discrete: Countable values (e.g., number of students)
    • Continuous: Any value within a range (e.g., income)

Example Explanation:

  • Continuous Variables: Detailed explanation using real-world examples.

Practical Example

Sales Comparison of Products

  • Columns: Product 1, Product 2, Product 3
  • Metrics: Average, Median, Standard Deviation, Coefficient of Variation
  • Conclusion: Product 2 is the most stable; Product 1 and 3 vary around their means.

Properties of Standard Normal Distribution

Key Points:

  1. Symmetry: Mean = Median = Mode
  2. Coverage:
    • 68% data within ±1 standard deviation
    • 95% data within ±2 standard deviations
    • 99.7% data within ±3 standard deviations

Examples of Hypothesis Testing

Steps:

  1. Formulation of Hypothesis
  2. Conducting Tests (Z-test, T-test, etc.)
  3. Conclusions

Examples Provided in Lecture:

  1. Testing average income claim
  2. Determining course effectiveness
  3. Comparing study techniques
  4. Unemployment rates
  5. Water quality testing

Types of Errors

  1. Type I Error (α): Rejecting a true null hypothesis
  2. Type II Error (β): Failing to reject a false null hypothesis