The IITM qualifier stats important questions are spread evenly over five topics: association between two variables, variance and percentiles, types of data and scales, categorical data, and mean, median and mode. We tagged every question in the five past Stats I qualifier papers on BTechi (74 questions, 200 marks). Each topic carries 16% to 24% of the marks. So unlike Maths I, you cannot skip any week. Every paper below is also a free Stats 1 qualifier PYQ PDF with the answer key.
The good news: Stats I questions repeat a lot. "Identify the scale of measurement" came up 5 times in 5 papers. This post gives you the data, the repeated question types, four real past-year questions solved step by step (checked against the official answer key), and the exact practice sheet for each topic.
New to the qualifier? Start with our IITM BS qualifier exam guide. It explains the process, the cut-offs and the four-week plan.
What the Stats I qualifier tests#
Stats I is "Statistics for Data Science I" (course code BSMA1002). The qualifier covers weeks 1 to 4 only. The official Stats I course page on study.iitm.ac.in lists the full syllabus. For the qualifier, these are the four weeks:
Permutations, probability, random variables and distributions are also in Stats I. But they come after week 4. In our tagging, not one qualifier question came from them. They appear in Stats I Quiz 1, Quiz 2 and the Stats I end term exam. Leave them for later.
To pass, a General-category candidate needs at least 40% in Stats I and at least 50% average across all four courses. Always check the current rules on the official IITM BS admissions page.
The 5 Stats I qualifier papers we analysed#
BTechi has five past Stats I qualifier papers. Each has the official answer key, and each can be taken in a timed exam portal.
Across these papers there are 28 numerical answer (NAT), 25 multiple-select (MSQ) and 21 single-correct (MCQ) questions. Many questions are 1 to 3 marks. So Stats I rewards speed and accuracy on many small questions, more than long calculations.
All Stats I papers (qualifier, quiz and end term) are on the Stats I PYQ page. For every qualifier paper across all four courses, see our post on the IITM qualifier previous year question paper with answer key.
Topic weightage: where the marks go#
We tagged each question to one topic and added up the marks per topic.
What this tells you:
- Week 4 (association) carries the most marks. Contingency tables, covariance, correlation and point bi-serial correlation give 47 marks. It is also the week students reach most tired. Plan extra time for it.
- Weeks 1 and 2 are cheap marks. Data types and categorical data have 34 questions between them, mostly 1 to 3 marks each. They are theory and chart reading. With practice, you can answer them in under a minute each.
- Week 3 has the traps. Variance, percentiles and outliers carry 42 marks. The IITM percentile method is different from what many school books teach. We solve one below.
The most repeated question types#
These question types came up in two or more of the five qualifier papers.
The Stats I most repeated PYQs sheet collects every repeated type into one printable sheet. It has 131 questions (355 marks) from all 13 Stats I papers on BTechi, with the official answer key at the end.
Solved IITM qualifier stats important questions#
Four real questions from past Stats I qualifier papers. Each final answer matches the official answer key in the paper data on BTechi.
Solved example 1: scales of measurement (May 2024, Q7, 3 marks)#
Question. Consider three statements:
- Statement 1: Election symbol is a categorical variable.
- Statement 2: Election symbol has a nominal scale of measurement.
- Statement 3: Number of votes received by a candidate is a continuous variable.
Which are correct? (a) 2 and 3, (b) 1 and 3, (c) 1 and 2, (d) all three.
Solution.
- An election symbol is a label. You cannot add it or average it. So it is categorical. Statement 1 is true.
- Symbols have no natural order. A lotus is not "more" than a hand. Labels with no order are nominal. Statement 2 is true.
- Votes are counted: 0, 1, 2, and so on. You cannot get 1,250.5 votes. Counts are discrete, not continuous. Statement 3 is false.
- Answer: (c) Statement 1 and Statement 2. The official key says (c).
The rule to remember: count = discrete, measure = continuous. Labels with no order = nominal. Labels with an order (like shirt size S, M, L) = ordinal. Practise on the data types and scales topic sheet.
Solved example 2: mode and median of ordinal data (January 2024, Q7 and Q8)#
Question. A survey of 10 students rated the quality of education as: Fair, Fair, Excellent, Poor, Fair, Excellent, Poor, Poor, Excellent, Poor. Find the mode (1 mark) and the median (2 marks).
Solution.
- Count each category. Poor = 4, Fair = 3, Excellent = 3.
- Mode is the most frequent category: Poor.
- For the median, the data must have an order. Poor < Fair < Excellent. So this is ordinal data, and the median is defined.
- Sort: Poor, Poor, Poor, Poor, Fair, Fair, Fair, Excellent, Excellent, Excellent.
- With 10 values, the median sits between the 5th and 6th values. Both are Fair. So the median is Fair.
Official key: mode Poor, median Fair. Both match.
The trap: for nominal data (like soft drink brands), the median is not defined, because there is no order. The May 2024 paper (Q1) tested exactly this: the correct options were "the data is bimodal" and "median is not defined". More of these are on the categorical data topic sheet.
Solved example 3: contingency table (May 2024, Q5 and Q6)#
Question. A survey of 32 college students (male and female) asks if they own a smartphone. 3 males do not own one. There are 27 females. In total, 26 students do not own a smartphone. (a) How many males own a smartphone? (b) Which statements are true?
- 40% of males do not own a smartphone.
- 14.81% of females own a smartphone.
- 18.75% of all students own a smartphone.
- We can use covariance to find the association between gender and smartphone ownership.
Solution. Build the two-way table first. Fill the given numbers, then use the totals.
- Males = 32 − 27 = 5. Males who own = 5 − 3 = 2. That answers (a).
- Females who do not own = 26 − 3 = 23. Females who own = 27 − 23 = 4. Total who own = 32 − 26 = 6.
- Males who do not own: 3/5 = 60%, not 40%. False.
- Females who own: 4/27 = 14.81%. True.
- All students who own: 6/32 = 18.75%. True.
- Gender and ownership are categorical. Covariance needs numbers. False. Use relative frequencies to judge association instead.
Official key: (a) 2; (b) the second and third statements. Both match.
The habit that wins: always draw the full table with totals before you read any option. Most wrong answers come from dividing by the wrong total (row total vs column total vs grand total). The association topic sheet has 20 questions to drill this.
Solved example 4: quartiles and outliers (May 2023, Q13 to Q15, 3 marks each)#
Question. Prices (in rupees) of 10 t-shirts: 150, 550, 700, 240, 300, 750, 200, 180, 320, 420. Find the price below which 25% of t-shirts fall, the price that separates the top 25%, and the number of outliers.
Solution. Use the IITM percentile method, which the official answer keys follow:
- Sort: 150, 180, 200, 240, 300, 320, 420, 550, 700, 750. Here n = 10.
- For the P-th percentile, find i = P × n / 100. If i is not a whole number, round up and take that value. If i is whole, average the values at positions i and i + 1.
- Q1 (25th percentile): i = 0.25 × 10 = 2.5. Round up to 3. The 3rd value is 200.
- Q3 (75th percentile): i = 0.75 × 10 = 7.5. Round up to 8. The 8th value is 550.
- IQR = 550 − 200 = 350. 1.5 × IQR = 525.
- Fences: lower = 200 − 525 = −325, upper = 550 + 525 = 1075. Every price is between them. Number of outliers = 0.
Official key: Q1 = Rs 200, Q3 = Rs 550, outliers = 0. All match.
The same method gives the September 2023 answer too: for 14, 20, 40, 23, 18, sorted as 14, 18, 20, 23, 40, Q1 is the 2nd value (18) and Q3 is the 4th (23), so IQR = 5. That matches the official key. Drill this on the dispersion and percentiles topic sheet.
Download IITM qualifier stats PYQ PDF with answer key#
- Open the question sheet of the paper you want (links below).
- Click the Save PDF button at the top of the sheet. You can also press P on your keyboard.
- In the print window, choose Save as PDF as the destination, then save.
The PDF has every question and figure, and the official answer key at the end. It is free. Print it, or keep it on your phone or tablet.
Want only the important questions as one PDF? Save the Stats 1 most repeated questions PDF. Each full paper as a PDF:
- Stats 1 qualifier May 2024 PDF with answer key
- Stats 1 qualifier January 2024 PDF with answer key
- Stats 1 qualifier September 2023 PDF with answer key
- Stats 1 qualifier May 2023 PDF with answer key
- Stats 1 qualifier January 2023 PDF with answer key
Rules to know cold for Stats I#
The linear-change rules alone cover three repeated types: mean after a change, variance after a change, and correlation with a linear function. Learn them once and you collect marks in almost every paper.
Our free Stats I cheat notes for the qualifier have every formula, the IITM percentile method, and more worked examples.
How to practise these important questions#
A plan built on the data above:
- Learn one week's topic from the lectures and the Stats I cheat notes.
- Solve the matching topic sheet on paper. Use the links in the topic table above. Check with the answer key at the end.
- Keep an error log. One line per mistake: which rule did you break? Two common ones in Stats I: "wrong total" and "wrong percentile position".
- After week 4, solve the Stats I most repeated PYQs sheet. This is your main revision document.
- Sit full papers under time. BTechi gives each Stats I paper 45 minutes. Start with the January 2023 Stats I qualifier paper and finish with the May 2024 Stats I qualifier paper. Or choose papers in the qualifier practice portal for Stats I.
- Finish with full four-course papers. Try the full May 2023 qualifier paper, the full September 2023 qualifier paper, then qualifier mock test 1 and mock test 2.
Prefer to print by year? Use the Stats I 2023 PYQ sheet and the Stats I 2024 PYQ sheet. All printable sheets are on the Stats I sheets page.
Mistakes that cost marks in Stats I#
- Median of nominal data. It is not defined. Only ordinal and numerical data have a median.
- Population vs sample variance. Divide by n for population, n − 1 for sample. The question always says which one. Read it.
- Wrong total in a contingency table. "Of all males" means divide by the male total, not the grand total.
- School percentile methods. Use the IITM method (round up the position). Other methods can give a different answer and lose the marks.
- Representative samples. A sample of only final-year students does not represent all students (September 2023, Q3). Check who is in the sample, not just its size.
Where Stats I fits in the qualifier#
Stats I is one of four qualifier courses. You need 40% in each and 50% average. Our companion post on IITM qualifier maths important questions does the same analysis for Maths I. To see every course and level in one place, read the IIT Madras BS data science PYQ guide or browse the Foundation level PYQs.
Planning to apply? The IIT Madras BS admission guide for January 2027 has the dates. Applications for the January 2027 batch close on 29 January 2027.
Frequently asked questions#
What are the most important topics for the IITM qualifier stats exam?#
Association between two variables (23.5% of marks), variance and percentiles (21%) and types of data and scales (20%), based on our tagging of five past Stats I qualifier papers. Categorical data (19.5%) and mean, median and mode (16%) are close behind. All five matter.
Where can I download the IITM qualifier stats important questions PDF?#
BTechi gives every Stats I qualifier paper as an online paper with the official answer key. It also gives printable sheets: open any Stats I PYQ sheet click Save PDF (or press P) and choose Save as PDF. For the important questions only, save the Stats I most repeated questions sheet as a PDF. The answer key is at the end of each sheet.
Are IITM qualifier stats questions repeated?#
Yes, a lot. "Identify the scale of measurement" appeared 5 times in 5 papers. Mode and median of ordinal data, and mean after a linear change, appeared 4 times each. In total, 16 question types appeared in two or more papers.
Is probability in the IITM qualifier stats syllabus?#
No. The qualifier covers weeks 1 to 4: types of data, categorical data, numerical data and association. In five past qualifier papers, no question came from probability, permutations or distributions. Those come later, in Stats I quizzes and the end term.
How many questions are in the Stats I qualifier paper?#
The five papers on BTechi have 13 to 18 Stats I questions each, worth 40 marks. They mix numerical answer, multiple-select and single-correct questions. The exact count and marking can change, so read the exam instructions on the day.
Which percentile method does IITM use in Stats I?#
Find the position i = P × n / 100 in the sorted data. If i is a fraction, round up and take that value. If i is a whole number, average the values at positions i and i + 1. The official answer keys follow this method.
Is Stats I easier than Maths I in the qualifier?#
Many students find Stats I more scoring, because many questions are short theory and chart questions. But it has more questions and more traps in percentiles and contingency tables. Do not take it lightly. You still need 40% in it to qualify.