BSMA1004 · 4 credits · Foundation
Statistics for
Data Science 2
The last Foundation course, and the first one that asks what you are entitled to conclude. Taught out of real IPL and height–weight data, with a Colab open next to the blackboard.
- Lectures
- 116 · 45 h
- Prerequisite
- Stats 1, Maths 1
- Co-requisite
- Maths 2
- Bonus marks
- up to 5
What this course actually asks
From describing to concludingStatistics 2 is taught by Andrew Thangaraj of the electrical engineering department at IIT Madras, and it is taught unusually: from data first. Casino odds, IPL scorecards, height and weight tables, with Colab illustrations alongside the derivations. If Statistics 1 felt abstract, this one will feel less so, not more.
The content is the real payload though. Weeks 1 to 5 extend probability to several variables at once and arrive at the limit theorems. Weeks 7 to 11 are inference — estimation, Bayesian estimation, and hypothesis testing. That is the first time the programme asks you to go from a sample to a claim about the world, with a stated chance of being wrong.
This is the course the Diploma quietly assumes. Estimators, likelihood, confidence and testing are the vocabulary of Machine Learning Foundations. Along with Maths 2, it is the most valuable Foundation course to actually understand rather than pass.
It has the heaviest requisite list in Foundation: Statistics 1 and Maths 1 must be done, and Maths 2 is a co-requisite — which is why the suggested pathway puts it last.
The twelve weeks
Topics quoted from the official course pageMultiple random variables. Two random variables; multiple random variables and distributions.
Independence; functions of random variables. Visualization, functions of multiple random variables.
Expectations. Casino math, expected value, scatter plots and spread, variance and standard deviation, covariance and correlation, inequalities.
Continuous random variables. Discrete vs continuous, weight data, density functions, expectations.
Multiple continuous random variables. Two continuous random variables, averages of random variables, limit theorems, IPL data, jointly Gaussian random variables, probability models for data.
Refresher week.
Estimation and inference I.
Estimation and inference II.
Bayesian estimation.
Hypothesis testing I.
Hypothesis testing II.
Revision week.
The whole inference half is outside the eligibility window
Eligibility closes at week 7. Estimation II, Bayesian estimation and both hypothesis-testing weeks all fall after it — and they are the majority of the end-term paper, and the part the Diploma needs.
Week 5, run rather than stated
Why inference works at allPick a source distribution — the uglier the better — and raise the sample size. The green bars are four thousand sample means actually computed; the purple curve is the normal distribution the limit theorem predicts. Start at n = 1, where they disagree completely, and watch what happens by n = 30.
Two things are happening at once. The shape becomes normal — that is the central limit theorem. And the spread shrinks like σ/√n — that is why quadrupling your sample only halves your error, and why every confidence interval in week 8 has a square root in it.
How it is graded
May 2026 grading document · confirm against your course pageThe standard formula, plus the same bonus structure as Statistics 1:
+ bonus for extra activity, capped at 5
The five bonus marks
Five extra activities across the term — in May 2026 they ran from week 1 onward, with a submission deadline and then a separate peer-review deadline about two weeks later. Worth 5 marks total: 3.75 for the activity and 1.25 for quality, at the instructors' discretion.
Five peer reviews, or the activity scores zero
The rule is identical to Statistics 1 and catches people just as often: submit the activity but complete fewer than five peer reviews and you are awarded 0 for it. The reviews have their own deadline, after the submission deadline — put both in your calendar.
The eligibility gate
Average of the best 5 of 8 — the first seven weekly assignments plus Mock Quiz 1 — must be 40/100 or more, and you must attend at least one quiz.
Where the marks actually go
My read, from this course and from what people ask aboutTreating week 6 as a holiday
The refresher week exists because the course knows the second half is harder. Spending it consolidating weeks 1–5 is worth more than any single week of new content.
Reading the p-value backwards
A p-value is the probability of data at least this extreme if the null hypothesis is true — not the probability that the null is true. Weeks 10 and 11 are written to catch the reversal.
Independence assumed, not checked
From week 2 onward, half the formulas only hold if the variables are independent. Questions supply dependent pairs on purpose. Check before you multiply.
Forgetting the peer reviews
Same as Statistics 1: five marks forfeited for a step that takes fifteen minutes and has its own separate deadline.
Everything worth opening
Official first, then the free things that genuinely helpEvery link here was opened and checked on 23 September 2026.
Official
- Course page BSMA1004 on study.iitm.ac.in The week list, the requisites, and the two joint-distribution volumes.
- Lectures Statistics for Data Science 2 — full playlist All 116 official lectures, including the IPL and Colab walkthroughs.
The book
- Free book Probability and Statistics with Examples using R The prescribed text by Athreya, Sarkar and Tanner, free from the authors. Its data-first approach is the same one the lectures take.
- Free book Introduction to Probability, Statistics and Random Processes Free and complete, with solved problems. Its chapters on joint distributions, limit theorems and estimation line up with weeks 1–9.
For the ideas
- Tool Seeing Theory · Brown University Its chapters on the central limit theorem, frequentist inference and Bayesian inference are weeks 5, 7–8 and 9, made draggable.
- Video StatQuest · Statistics Fundamentals The clearest short explanations of p-values, confidence intervals and hypothesis testing anywhere. Use it for weeks 10 and 11.
- Free book OpenIntro Statistics Its inference chapters are gentler than the lectures and full of worked examples. Good first pass before the formal treatment.
What to do in week one
Term starts 2 October 2026- Find the five activity deadlinesBoth dates for each — submission, and then peer review. Five marks, and the most commonly forfeited five in Foundation.
- Make sure Stats 1 is solidExpectation, variance and conditional probability are assumed from lecture one, not re-taught.
- Open a ColabThe lectures use one. Following along with the IPL and height–weight data is the difference between watching and learning.
- Do not coast to week 6Week 5 is the densest in the course. If it is shaky, the refresher week is your one chance to fix it before inference starts.
- Plan for weeks 7–11 outside the gateAll of inference sits after eligibility closes, and it is most of the end term.
- Check your course page's grading sectionEverything here is from the May 2026 document. The September 2026 one was not published when this was written.