IITM BS Statistics 1 and 2: How to Improve Your Scores

To improve in IITM BS Statistics, solve small problems by hand every week, and learn to spot which kind of question you are looking at. Statistics 1 (BSMA1002) goes from describing data to probability and random variables. Statistics 2 (BSMA1004) builds on it with several random variables, estimation and hypothesis testing. Marks are usually lost in setting a problem up, not in the arithmetic.

What Statistics 1 covers

Weeks 1 to 4 are descriptive statistics. Weeks 5 to 12 are counting and probability. Give these weeks the most practice time. For a quick overview, see our Statistics 1 subject page.

What Statistics 2 covers

Statistics 2 needs Statistics 1, and its course page also lists Maths 1 as a prerequisite. Maths 2 is a corequisite, so take it before Stats 2 or in the same term.

Use the refresher and revision weeks as real work weeks. They are your chance to catch up before the second half.

How to practise each type of topic

Describing data

Work with tiny data sets by hand. Take 2, 3, 3, 4 and 38. The mean is 10 but the median is 3. That one extreme value pulls the mean far away, which is why the median is often the better summary for skewed data. Always check whether a question wants the population or the sample version of variance.

Counting

Before you touch a formula, ask two questions. Does order matter? Can items repeat? Arranging 5 people in a row gives 5 x 4 x 3 x 2 x 1 = 120 ways. Choosing 2 of those 5 for a team is 10, because order does not matter. Write the answer to both questions in the margin every time.

Conditional probability and Bayes

Turn percentages into counts. Say 1% of 10,000 people have a condition. A test catches 90% of real cases and wrongly flags 5% of healthy people.

• 100 people have it, and 90 of them test positive.
• 9,900 do not, and 495 of them test positive.
• So a positive result means the condition only 90 out of 585 times, about 15%.

A count table like this avoids most Bayes mistakes.

Random variables and distributions

Write the probability table first, and check that it adds up to 1. For a fair die, the expected value is 3.5. For a binomial question, name n and p before you do anything else. With n = 4 and p = 0.5, the chance of exactly 2 successes is 6/16.

Statistics 2 topics

• For two random variables, draw the joint table and find each marginal by adding rows and columns.
• Independence has a clear test: every joint probability must equal the product of its marginals. One failed cell is enough to say no.
• Remember that Var(X+Y) = Var(X) + Var(Y) + 2 Cov(X,Y). The covariance term drops out only when X and Y are uncorrelated.
• For continuous variables, you will integrate a density. Weak integration shows up here, so revise week 9 of our Maths 1 guide early.
• For hypothesis testing, write the null and alternative hypotheses in words before any numbers.

A weekly routine for both courses

1. Watch the week's videos and answer the self-test after each one.
2. Solve the practice assignment on paper first, then check the solutions the handbook says are released with it.
3. Keep a one-page "question types" sheet. Add each new type with one tiny example you made up.
4. Do the graded assignment on your own. Sharing or copying answers breaks the honour code.
5. Before each quiz, redo the practice assignments of every week in the quiz syllabus under a timer.

Using the official books and notes

The Statistics 1 course page offers two volumes to download: Descriptive Statistics, and Probability and Probability Distributions. Its suggested books are Introductory Statistics by Neil A. Weiss and Introductory Statistics by Sheldon M. Ross. Statistics 2 offers volumes on joint discrete and joint continuous distributions, and suggests Probability and Statistics with Examples using R by Athreya, Sarkar and Tanner.

Common questions

Is Statistics 2 harder than Statistics 1?

It uses more maths. Joint distributions, continuous variables and estimation lean on calculus and algebra from Maths 1 and Maths 2. If your Maths 1 grade was weak, plan more hours for Stats 2.

Should I take Stats 2 with Maths 2?

You may, since Maths 2 is a corequisite. Whether you should depends on your hours and your Maths 1 comfort. Our post on Maths 2 and Stats 2 in the same term walks through it.

I cleared the Stats 1 part of the qualifier easily. Can I relax?

No. The qualifier covers only the early weeks, which are mostly descriptive. Counting and probability start later and need more practice. Our qualifier statistics tips list common early mistakes.

Do I need software for these courses?

The Statistics 2 page mentions a Colab illustration and data sets such as IPL data in week 5, and its suggested book uses R. Your grading document and course portal tell you what is required. Keep most of your practice on paper.