Statistics for Data Science I

An introduction to the foundational concepts of statistics, from describing data and understanding probability to working with random variables.

Statistics for Data Science I provided the fundamental building blocks for understanding and interpreting data. The course introduced me to the complete data analysis pipeline, starting from identifying different types of data and their measurement scales. I learned to summarize and visualize both categorical and numerical data using various descriptive statistics and graphical methods. A significant portion of the course was dedicated to building a strong foundation in probability theory, from basic counting principles to conditional probability and Bayes’ theorem, which paved the way for understanding and working with random variables and their distributions.

Instructor

Prof. Usha Mohan, Department of Management Studies, IIT Madras

Course Schedule & Topics

The course is structured over 12 weeks, covering the core principles of probability and descriptive statistics.

Week Primary Focus Key Topics Covered
1 Data Fundamentals Introduction and type of data, Descriptive and Inferential statistics, Scales of measurement.
2 Categorical Data Analysis Describing categorical data, Frequency distribution, Best practices for graphing, Mode and median for categorical variables.
3 Numerical Data Analysis Frequency tables, Measures of central tendency (Mean, Median, Mode), Quartiles and percentiles, Measures of dispersion (Range, Variance, Std. Dev, IQR), Five-number summary.
4 Relationships Between Variables Association between categorical variables (contingency tables), Association between numerical variables (Scatterplot, Covariance, Pearson correlation).
5 Principles of Counting Basic principles of counting, Addition rule, Multiplication rule, and factorial concepts.
6 Permutations & Combinations Detailed exploration of permutations and combinations.
7 Foundations of Probability Basic definitions of probability, Sample space, Events, and fundamental properties of probability.
8 Conditional Probability Multiplication rule, Independence, Law of total probability, and Bayes’ theorem.
9 Intro to Random Variables Random experiment, sample space, discrete and continuous random variables, Probability Mass Function (PMF), Cumulative Density Function (CDF).
10 Properties of Random Variables Expectation of a discrete random variable ($E[X]$), Variance ($\text{Var}(X)$), and Standard Deviation ($\sigma$) of a discrete random variable.
11 Common Discrete Distributions Bernoulli trials, Binomial random variable, Poisson distribution, Geometric distribution, and Negative binomial distribution.
12 Common Continuous Distributions Introduction to continuous random variables, Probability Density Functions (PDF), Uniform distribution, Exponential distribution, and Normal distribution.

Material used