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Stats I · All 2024 papers

BSMA1002 · 66 questions · 180 marks · 4 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

All 2024 papers

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q1–Q2
Based on the above data answer the given subquestions.
Q1MCQ3 Marks·Choose one option
Asked 6 times Key ↓
What is the difference between the expenditure on Rent and Groceries?
1. A₹2000
2. B₹2500
3. C₹1500
4. D₹2700
Q2MCQ2 Marks·Choose one option
Asked 6 times Key ↓
How much money does the family spend on Utilities and Entertainment combined?
1. A₹12,000
2. B₹12,500
3. C₹15,000
4. D₹15,200
Q3MSQ2 Marks·Choose all correct options
Asked 5 times Key ↓
Which of the following options is/are incorrect for a variable having ratio scale of measurement?
1. ADifference between the values of a variable can not be evaluated.
2. BOrder of the data is meaningful.
3. CMultiplication and division of values of a variable is possible.
4. DIt does not have an absolute zero.
Q4NAT4 Marks·Write the number
Asked 5 times Key ↓
The average of 15 observations is 48. If the average of the first 8 observations is 42 and the average of the last 8 observations is 54, what is the value of the 8th observation?
Your answer:
Q5NAT4 Marks·Write the number
Asked 2 times Key ↓
A certain type of electronic device has a lifetime that follows an exponential distribution with a mean of 500 hours. If the device has already worked for 300 hours without failing, what is the probability that it will continue to function for at least another 200 hours? (Enter the answer correct to 2 decimal accuracy.)
Your answer:
Read the passage below, then answer Q6–Q7
A university needs to form a research team of 4 students out of total 8 students.
Based on the above data answer the given subquestions.
Q6NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q7NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:
Q8NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word “LEADING” be arranged such that the vowels always come together?
Your answer:
Q9NAT2 Marks·Write the number
Asked 3 times Key ↓
In a survey of 100 people, 60 like tea, 40 like coffee, and 20 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q10MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
A jar contains 5 red balls and 7 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D
Q11MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q12–Q13
Based on the above data answer the given subquestions.
Q12MCQ4 Marks·Choose one option
Asked 5 times Key ↓
1. A15
2. B10
3. C20
4. D12
Q13NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q14MCQ3 Marks·Choose one option
Asked 3 times Key ↓
If the Indian cricket team has a 60% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
1. A0.26
2. B0.078
3. C0.34
4. D0.68
Q15MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A{0,1,2,3,4}
2. B{0,1,2,3}
3. C{0,1,2}
4. D{0,1,2,3,4,5}
Q16MCQ4 Marks·Choose one option
Asked 4 times Key ↓
The number of customers entering in a store follows a Poisson distribution with an average rate of 12 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
1. A
2. B
3. C
4. D
Q17MCQ4 Marks·Choose one option
Asked 4 times Key ↓
Metros on a certain station arrives uniformly after every 5 minutes. If a person arrives at the metro station at random, then what is the probability that he has to wait at least 3 minutes?
1. A
2. B
3. C
4. D

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q18–Q19
Based on the above data answer the given subquestions.
Q18MCQ3 Marks·Choose one option
Asked 6 times Key ↓
What is the difference between the expenditure on Groceries and Utilities?
1. A₹20000
2. B₹12500
3. C₹15000
4. D₹27000
Q19MCQ2 Marks·Choose one option
Asked 6 times Key ↓
How much money does the family spend on Rent and Utilities combined?
1. A₹25,000
2. B₹27,500
3. C₹27,000
4. D₹28,000
Q20MSQ2 Marks·Choose all correct options
Asked 5 times Key ↓
Which of the following options is/are incorrect for a variable having ratio scale of measurement?
1. ADifference between the values of a variable can not be evaluated.
2. BOrder of the data is meaningful.
3. CMultiplication and division of values of a variable is possible.
4. DIt does not have an absolute zero.
Q21NAT4 Marks·Write the number
Asked 5 times Key ↓
The average of 15 observations is 45. If the average of the first 8 observations is 41 and the average of the last 8 observations is 53, what is the value of the 8th observation?
Your answer:
Q22NAT4 Marks·Write the number
Asked 2 times Key ↓
A certain type of electronic device has a lifetime that follows an exponential distribution with a mean of 500 hours. If the device has already worked for 400 hours without failing, what is the probability that it will continue to function for at least another 100 hours? (Enter the answer correct to 2 decimal accuracy.)
Your answer:
Read the passage below, then answer Q23–Q24
A university needs to form a research team of 4 students out of total 9 students.
Based on the above data answer the given subquestions.
Q23NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must be included?
Your answer:
Q24NAT2 Marks·Write the number
Asked 4 times Key ↓
In how many ways can the team be formed if two particular students must not be included?
Your answer:
Q25NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word “READING” be arranged such that the vowels always come together?
Your answer:
Q26NAT2 Marks·Write the number
Asked 3 times Key ↓
In a survey of 120 people, 70 like tea, 50 like coffee, and 30 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q27MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
A jar contains 6 red balls and 8 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D
Q28MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q29–Q30
Based on the above data answer the given subquestions.
Q29MCQ4 Marks·Choose one option
Asked 5 times Key ↓
1. A15
2. B10
3. C20
4. D12
Q30NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q31MCQ3 Marks·Choose one option
Asked 3 times Key ↓
If the Indian cricket team has a 65% chance of winning a match, and they play a 5-match series with each match being independent of the others, what is the probability that the team will win at least 4 matches?
1. A0.31
2. B0.12
3. C0.43
4. D0.57
Q32MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A{0,1,2,3,4}
2. B{0,1,2,3}
3. C{0,1,2}
4. D{0,1,2,3,4,5}
Q33MCQ4 Marks·Choose one option
Asked 4 times Key ↓
The number of customers entering in a store follows a Poisson distribution with an average rate of 8 customers per hour. What is the probability that exactly 5 customers will enter the store in a 15- minute period?
1. A
2. B
3. C
4. D
Q34MCQ4 Marks·Choose one option
Asked 4 times Key ↓
Metros on a certain station arrives uniformly after every 10 minutes. If a person arrives at the metro station at random, then what is the probability that he has to wait at least 4 minutes?
1. A
2. B
3. C
4. D

Qualifier · May 2024Qualifier

Q35MSQ2 Marks·Choose all correct options
Asked 4 times Key ↓
Figure Q.1 shows the sales distribution of the number of bottles of different types of soft drinks in a shop on a particular day. Which of the following option(s) is/are true?
1. AMedian of the data will be either “Mountain Dew” or “Mirinda”.
2. BThe data is bimodal.
3. CMode is not defined for the given data.
4. DMedian is not defined for the given data.
Q36MSQ2 Marks·Choose all correct options
Key ↓
Which of the following statement(s) is/are true?
1. AStructured data does not follow a predefined format, whereas unstructured data does.
2. BRecording of the data over time comes under Cross Sectional data.
3. CTime (in minutes) taken by a student to reach school from his home is a continuous variable.
4. DComments on a youtube video comes under the unstructured data.
Read the passage below, then answer Q37–Q38
Table Q.1 represents the number of books read by five students in a year.
Based on the above data, answer the given subquestions
Q37NAT2 Marks·Write the number
Asked 5 times Key ↓
What is the value of x? Enter the answer correct to two decimal places.
Your answer:
Q38MCQ3 Marks·Choose one option
Key ↓
If the number of books read by Prateek is same as the number of books read by Sonakshi, then find the value of y + z.
1. A0.2
2. B0.24
3. C0.4
4. DInsufficient information.
Read the passage below, then answer Q39–Q40
Amit took a survey of a group of 32 college going students (consisting only of male and female students) to know whether they own a smartphone or not and he got to know the following information.
(i). There are 3 males who do not own a smartphone.
(ii). There are total 27 females.
(iii). There are total 26 students who do not own a smartphone.
Based on the above information, answer the given subquestions.
Q39MCQ2 Marks·Choose one option
Key ↓
Create a two-way contingency table and find out the number of males in this group who own a smartphone?
1. A0
2. B2
3. C3
4. D4
Q40MSQ3 Marks·Choose all correct options
Key ↓
Choose the correct option(s) after making a two-way contingency table.
1. AThere are 40% of the males who do not own a smartphone.
2. BThere are 14.81% of the females who own a smartphone.
3. C18.75% of the total students own a smartphone.
4. DWe can calculate covariance to find the association between “Gender” and “Ownership of the smartphone”.
Q41MCQ3 Marks·Choose one option
Asked 6 times Key ↓
Consider the following 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. Choose the correct option from the following:
1. AStatement-2 and statement-3 both are correct.
2. BStatement-1 and statement-3 both are correct.
3. CStatement-1 and statement-2 both are correct.
4. DAll statements are correct.
Q42MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Choose the correct statement from the following:
1. ADescriptive statistics is concerned with drawing of conclusions from the sample data.
2. BInferential statistics is concerned with describing and summarizing the data.
3. CInferential statistics doesn’t require sample data.
4. DAll statements are incorrect.
Q43MCQ2 Marks·Choose one option
Key ↓
Consider the following four images of the Scatter plot. Please select the option that will represent the correlation values arranged in ascending order.
1. AA < B < C < D
2. BB < C < D < A
3. CB < A < C < D
4. DA < D < C < B
Q44NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q45NAT3 Marks·Write the number
Asked 4 times Key ↓
Find the population covariance between X and Y for the dataset given in Table Q.2.
Your answer:
Read the passage below, then answer Q46–Q48
The marks (out of 100) scored by Manoj in a semester exam are given as 60, 70, 65, 75, 80. If Nitin has scored 5 marks more than Manoj in each subject.
Based on the given information, answer the subquestions.
Q46NAT2 Marks·Write the number
Asked 4 times Key ↓
Find the mean of the marks scored by Nitin.
Your answer:
Q47MCQ4 Marks·Choose one option
Asked 4 times Key ↓
1. A25
2. B50
3. C12.5
4. DCannot determine
Q48NAT2 Marks·Write the number
Asked 2 times Key ↓
Calculate the correlation coefficient between the marks scored by Manoj and Nitin.
Your answer:
Read the passage below, then answer Q49–Q50
Based on the above data, answer the given subquestions
Q49NAT2 Marks·Write the number
Asked 3 times Key ↓
What will be the median age for this group?
Your answer:
Q50NAT1 Mark·Write the number
Key ↓
How many people are above 23 years of Age in the given stem and leaf plot?
Your answer:
Q51NAT1 Mark·Write the number
Asked 4 times Key ↓
Your answer:
Q52MSQ1 Mark·Choose all correct options
Key ↓
Choose the correct option(s):
1. A25th percentile is known as the first quartile.
2. BMedian is the 60th percentile of any data.
3. CInter-quartile range is defined as the difference between third quartile and second quartile.
4. DWe need to arrange the data in ascending order to calculate the percentile.

Qualifier · January 2024Qualifier

Q53MCQ2 Marks·Choose one option
Asked 4 times Key ↓
1. AThere is an association between “Gender” and “Willingness” as row relative frequencies will be approximately same for all rows.
2. BThere is no association between “Gender” and “Willingness” as row relative frequencies will be approximately same for all rows.
3. CThere is an association between “Gender” and “Willingness” as row relative frequencies will be different for all rows.
4. DThere is no association between “Gender” and “Willingness” as row relative frequencies will be different for all rows.
Q54MSQ4 Marks·Choose all correct options
Key ↓
1. AThere are 9 students who have scored greater than 20 marks.
2. BThe data is bimodal.
3. CMean is greater than the median.
4. DInterquartile range is 28.
Q55NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q56NAT4 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q57MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
To ensure the accuracy of conclusions drawn through inferential statistics, which of the following statement(s) must be true?
1. ASample should not be randomly selected.
2. BSample should be randomly selected.
3. CSample should be a good representative of the population.
4. DSample should not be representative of the population.
Q58MSQ2 Marks·Choose all correct options
Asked 6 times Key ↓
Which of the following statement(s) is/are true?
1. AThe gross annual income for each of 1000 randomly chosen households in New York City for the year 2000 is a time series data.
2. BPassenger Name Record (PNR) number has an ordinal scale of measurement.
3. CRevenue generated by India through tea exports to 10 different countries in year 2010 is a cross-sectional data.
4. DShirt size is a categorical variable.
Read the passage below, then answer Q59–Q60
An analyst conducted a survey to understand the opinions of college students regarding the quality of education at their institution. He collected the data from 10 students as:
“Fair”, “Fair”, ”Excellent”, “Poor”, “Fair”, “Excellent”, “Poor”, “Poor”, “Excellent”, and “Poor”.
Based on the above data, answer the given subquestions.
Q59MCQ1 Mark·Choose one option
Asked 4 times Key ↓
What is the mode of the given data?
1. AExcellent
2. BPoor
3. CFair
4. DMode is not defined for the given data
Q60MCQ2 Marks·Choose one option
Asked 4 times Key ↓
What is the median of the given data?
1. APoor
2. BFair
3. CExcellent
4. DMedian is not defined for given data
Q61MSQ5 Marks·Choose all correct options
Asked 4 times Key ↓
1. AOf all the shirts with Polo style, there are 26.67% shirts of Medium size.
2. BOf all the shirts with Small size, there are 25% shirts of Small Print style.
3. CThere is no association between the size and style of shirts.
4. DThere is an association between the size and style of shirts.
Q62MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q63MCQ3 Marks·Choose one option
Key ↓
Select the correct statements from the following:
1. ATwo data sets with the identical frequency distributions will have identical relative frequency distributions.
2. BA relative frequency is the number of observations belonging to a category.
3. CTwo data sets with the identical relative-frequency distributions will always have identical frequency distributions.
4. DIf all of the bars in a bar chart have the same length, then the categorical variable shown in the bar chart has no variation.
Read the passage below, then answer Q64–Q65
Q64NAT2 Marks·Write the number
Key ↓
Find the value of 10x.
Your answer:
Q65MSQ3 Marks·Choose all correct options
Key ↓
Choose the correct statement(s) from the following.
1. AMode of the data is solar energy.
2. BMedian of the data is wind energy.
3. CThe combined consumption of the hydro, biomass and geothermal energy is more than the wind energy consumption.
4. DThe consumption of solar energy is 120 kWh.
Q66MSQ3 Marks·Choose all correct options
Asked 6 times Key ↓
1. APurchase and Region are categorical variables.
2. BIncome Range has nominal scale of measurement.
3. CAge has a ratio scale of measurement.
4. DHousehold size is a discrete numerical variable.
5. EPurchase has an ordinal scale of measurement.

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1B

Q2B

Q3A, D

Q448

Q50.64 to 0.7

Q615

Q715

Q8720

Q90.8

Q10A, C

Q11A, D

Q12B

Q131.01 to 1.07

Q14C

Q15A

Q16D

Q17B

Q18B

Q19B

Q20A, D

Q2177

Q220.79 to 0.85

Q2321

Q2435

Q25720

Q260.72 to 0.78

Q27A, C

Q28A, D

Q29B

Q301.01 to 1.07

Q31C

Q32A

Q33D

Q34B

Q35B, D

Q36C, D

Q370.23 to 0.27

Q38C

Q39B

Q40B, C

Q41C

Q42D

Q43B

Q449.9 to 9.96

Q450

Q4675

Q47C

Q481

Q4931

Q508

Q5190

Q52A, D

Q53B

Q54C, D

Q5539

Q5670

Q57B, C

Q58C, D

Q59B

Q60B

Q61A, D

Q62C

Q63A

Q64357

Q65A, C

Q66A, C, D

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.