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Stats I · All 2023 papers

BSMA1002 · 42 questions · 120 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

All 2023 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.

Qualifier · September 2023Qualifier

Q1NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q2–Q3
The Head of the transportation facility at the IIT Madras campus wants to conduct a survey to rate the bus services offered to all the students. He randomly selects 100 final year students from the campus. Based on the given information, answer the subquestions
Q2MSQ3 Marks·Choose all correct options
Key ↓
Identify the sample and the population.
1. AThe population is all the students at IIT Madras campus.
2. BThe sample is all the final year students at IIT Madras campus.
3. CThe sample is 100 randomly selected final year students at IIT Madras campus.
4. DThe population is all the final year students at IIT Madras campus.
Q3MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Identify the correct statement from the following.
1. ASelected sample is a good representation of the population.
2. BSelected sample is not a good representation of the population.
Read the passage below, then answer Q4–Q5
Q4NAT2 Marks·Write the number
Asked 6 times Key ↓
If a total of 500 fruits are sold on a given day, then find the number of mangoes sold.
Your answer:
Q5MSQ3 Marks·Choose all correct options
Key ↓
Choose the correct statement(s) from the following.
1. AThe slices of pie chart adds up to 100%.
2. BMedian of the data is Grapes.
3. CMode of the data is Guava.
4. DThe pie chart is misleading because it does not obey the area principle.
Read the passage below, then answer Q6–Q7
Q6NAT5 Marks·Write the number
Key ↓
Calculate the absolute value of Point Bi-serial correlation coefficient between the result and number of hours spent. Enter the answer correct to three decimal places.
Your answer:
Q7MCQ2 Marks·Choose one option
Key ↓
Are the exam results of the selected students strongly influenced by the number of hours spent studying?
1. AYes, because the absolute value of Point Bi-serial coefficient is close to 1.
2. BNo, because the absolute value of Point Bi-serial coefficient is close to 1.
3. CYes, because the absolute value of Point Bi-serial coefficient is close to 0.
4. DNo, because the absolute value of Point Bi-serial coefficient is close to 0.
Read the passage below, then answer Q8–Q9
Q8NAT3 Marks·Write the number
Asked 4 times Key ↓
What is the average annual package of the students if each observation is doubled after subtracting 5 from it?
Your answer:
Q9MCQ4 Marks·Choose one option
Asked 4 times Key ↓
What is the population variance of the given data if 5 is subtracted from each observations?
1. A78.6
2. B83.6
3. C88.6
4. D93.6
Q10NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q11MSQ2 Marks·Choose all correct options
Asked 6 times Key ↓
Which of the following statement(s) is(are) true?
1. AEye colour of a person has ordinal scale of measurement.
2. BRecording the price of bitcoin every hour for 3 days is a time-series data.
3. CNumber of students present in a class is a discrete variable.
4. DAmount of milk (in litres) is a categorical variable.
Q12MSQ2 Marks·Choose all correct options
Asked 4 times Key ↓
Sunidhi purchased 5 t-shirts of sizes M, L, S, XL, S for her cousins. Later she purchased one more t-shirt of size M, then choose the correct option(s) from the following:
1. AMedian of the new data is same as of old data.
2. BNew data will be bimodal.
3. CMedian of the new data will change.
4. DNew data will be unimodal.
Q13MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q14NAT2 Marks·Write the number
Asked 3 times Key ↓
Find the IQR (Interquartile range) of the data 14, 20, 40, 23 and 18.
Your answer:

Qualifier · May 2023Qualifier

Q15MCQ2 Marks·Choose one option
Asked 4 times Key ↓
A researcher wants to investigate the relationship between studying hours and exam scores. He collects the data on studying hours and exam scores from a sample of 100 students and perform a correlation analysis. Which branch of statistics does this analysis belong to?
1. ADescriptive Statistics.
2. BInferential Statistics.
3. CBoth Descriptive and Inferential Statistics.
4. DNeither Descriptive nor Inferential Statistics.
Q16MSQ2 Marks·Choose all correct options
Asked 3 times Key ↓
1. AIt is a time series Data.
2. BIt is a cross sectional Data.
3. CIt is a structured Data.
4. DIt is an unstructured Data.
Q17MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following is/are correct?
1. AMean and Mode can only be defined for a numerical data.
2. BMode can be defined for a categorical data.
3. CThere can be more than one mode for a data.
4. DMedian can be measured for a categorical variable only if the variable is nominal.
5. EThe sum of relative frequencies of all the observations in a given data set is always equal to 1.
Q18NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q19NAT4 Marks·Write the number
Key ↓
The mean and sample variance of the data set consisting of 10 observations is 22 and 81 respectively. Later it is noted that one observation 20 is wrongly noted as 15. what is the sample standard deviation of the original data set?(Enter the answer correct to two decimal accuracy)
Your answer:
Read the passage below, then answer Q20–Q22
Table 2 represents the movies released in 2022 on the OTT platform.
Based on the information, answer the given subquestions.
Q20NAT2 Marks·Write the number
Key ↓
Find the total number of released movies in 2022 on OTT Platform.
Your answer:
Q21NAT2 Marks·Write the number
Key ↓
Find the number of Thriller and Comedy movies released in 2022 on OTT Platform.
Your answer:
Q22NAT3 Marks·Write the number
Asked 5 times Key ↓
Calculate a + b. (Enter the answer correct to three decimal accuracy)
Your answer:
Read the passage below, then answer Q23–Q24
Based on the given data in the Table 3 , answer the subquestions.
Q23MSQ2 Marks·Choose all correct options
Key ↓
Which of the following statements is/are true?
1. AXYZ Ltd. is a variable.
2. BNumber of employees have a ratio scale of measurement.
3. CGrowth Rate (%) is a variable.
4. DCategory have an interval scale of measurement.
Q24MCQ2 Marks·Choose one option
Asked 6 times Key ↓
What is the scale of measurement of “Category”?
1. AOrdinal Scale.
2. BRatio Scale.
3. CNominal Scale.
4. DInterval Scale.
Read the passage below, then answer Q25–Q26
Table 5 represents the data set about Advertising Expenditure and the Sales Revenue of a company. An analyst wants to investigate the relationship between the Advertising Expenditure (in Lakhs of rupees) and the monthly Sales Revenue (in Lakhs of rupees) of a company over a period of 6 months.
Based on the information, answer the given subquestions.
Q25MSQ2 Marks·Choose all correct options
Key ↓
Which measure(s) will help you to determine the existence of the relation between Sales Revenue and the Advertising Expenses?
1. ACovariance
2. BMean of both Sales and Advertising
3. CCorrelation Coefficient
4. DNone
Q26NAT4 Marks·Write the number
Asked 4 times Key ↓
What is the sample covariance between the Sales Revenue and Advertising Expenses?(Enter the answer correct to one decimal accuracy)
Your answer:
Read the passage below, then answer Q27–Q29
A clothe retailer wants to analyze the prices of different brands of t-shirts in his store. He randomly collected 10 t-shirts and prices (in rupees) of the t-shirts are 150, 550, 700, 240, 300, 750, 200, 180, 320, 420 respectively.
Based on the information, answer the given subquestions.
Q27MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Price below which 25% of the t-shirts fall.
1. AIt is a measure of Q₁.
2. B200 Rs.
3. CIt is a measure of Q₃.
4. D550 Rs.
Q28MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Price of the t-shirt that separates price of the highest 25% of the data from the lower 75%.
1. AIt is a measure of Q₂
2. B550 Rupees
3. CIt is a measure of Q₃
4. D310 Rupees
Q29MCQ3 Marks·Choose one option
Asked 3 times Key ↓
How many outliers are in the given data set?
1. A0
2. B1
3. C2
4. DCan’t determined.

Qualifier · January 2023Qualifier

Read the passage below, then answer Q30–Q31
Figure Q.1 represents the placement report of an engineering college for the academic year 2021-22.
Based on the information, answer the given subquestions.
Q30MCQ2 Marks·Choose one option
Key ↓
Which of the following category does not represent the mode?
1. AAnalytics
2. BSoftware
3. CCore
4. DInsufficient information
Q31NAT3 Marks·Write the number
Asked 6 times Key ↓
If 1200 students are placed during the placement season of 2021-22, then find the number of students placed in core companies?
Your answer:
Q32MSQ3 Marks·Choose all correct options
Key ↓
Which of the following statements is/are true?
1. AA sample is the subset of a population.
2. BNumerical variables can have all the properties of ordinal and nominal scales of measurement.
3. CCategorical variable can have numerical properties.
4. DCorrelation coefficient measures a linear association between two numerical variables.
Q33MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following represent(s) cross sectional data?
1. ACensus of tigers estimated in four different countries in 2021.
2. BYearly irrigation report released by a government over the period of ten years.
3. CRevenue generated by a company in four different states in 2022.
4. DMonthly expenditure of a family in 2020.
Q34MSQ3 Marks·Choose all correct options
Asked 5 times Key ↓
Choose the correct statement/s ?
1. AA nominal scale has the property of labelling the categories and it does not involve the ranking of data.
2. BAn ordinal scale has all the properties of nominal scale and it involves the ranking of data.
3. CAn Interval scale has all the properties of ordinal scale and it satisfies the absolute zero property.
4. DA ratio scale has all the properties of interval scale and it does not satisfy the absolute zero property.
Q35MCQ4 Marks·Choose one option
Asked 3 times Key ↓
Suppose the number of cars sold by a car dealer in five months are 12, 8, 9, 20, 40. Which of the following is/are outliers?
1. A-8
2. B20
3. C40
4. D8
Q36MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
An analyst did a survey to know whether literacy rate affects voting rate among adults in villages. He collected the data from a village and the results are tabulated in Table Q.1. Choose the correct option/s?
1. AOf all the literate adults, 25% do not participate in voting.
2. BOf all the illiterate adults, 72.73% participate in voting.
3. CIf all row relative frequencies are similar within each column then, it implies that all column relative frequencies will also be similar within each row.
4. DIf all column relative frequencies are similar within each row then, it does not imply that all row relative frequencies will also be similar within each column.
5. EThere is no association between literacy and voting participation.
6. FThere is an association between literacy and voting participation.
Read the passage below, then answer Q37–Q38
An analyst want to analyse the salary of employees in different organizations in a city. To analyse this, he has selected an organization and the data of salaries is tabulated as shown in Table Q.2.
Based on the given information, answer the subquestions.
Q37MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Based on the data collected from an organisation, analyst made a statement that the average salary of an employee is 50,000 rupees in different organizations in the city. The given statement of analyst is based on which kind of statistical analysis ?
1. ADescriptive statistics
2. BInferential statistics
Q38NAT4 Marks·Write the number
Key ↓
What is the sample standard deviation of salary (in thousand rupees)? (Enter the answer correct to 2 decimal accuracy)
Your answer:
Read the passage below, then answer Q39–Q40
The heights (in cm) of ten athletes are represented by a stem and leaf plot in Figure Q.2.
Based on the above information, answer the given subquestions
Q39NAT3 Marks·Write the number
Asked 3 times Key ↓
What is the median height(in cm) of an athlete?
Your answer:
Q40NAT3 Marks·Write the number
Asked 3 times Key ↓
What is the mode of the heights (in cm) of athletes?
Your answer:
Q41NAT3 Marks·Write the number
Asked 4 times Key ↓
The mean and sample variance of the marks (out of 50) scored by the students in the Statistics course are 40 and 25 respectively. If 5 is subtracted from the marks of each student and then multiplied by 2. Find the mean of the modified marks.
Your answer:
Q42MCQ3 Marks·Choose one option
Asked 2 times Key ↓
Let X and Y represent the total marks of Mayur and Deepak in 5 subjects respectively. If the marks scored by Deepak is twice the marks scored by Mayur in each subject, then which of the following statement is correct?
1. AThere is no correlation between X and Y .
2. BThere is a weak positive correlation between X and Y .
3. CThere is a strong positive correlation between X and Y .
4. DInsufficient information.

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q110

Q2A, C

Q3B

Q4125

Q5A, C

Q60.04 to 0.05

Q7D

Q840

Q9C

Q100.29 to 0.35

Q11B, C

Q12A, B

Q13B, D

Q145

Q15A

Q16A, C

Q17B, C, E

Q185

Q198.68 to 8.71

Q20200

Q2137

Q220.542 to 0.548

Q23B, C

Q24C

Q25A, C

Q2618.6 to 19.2

Q27A, B

Q28B, C

Q29A

Q30C

Q31300

Q32A, B, D

Q33A, C

Q34A, B

Q35C

Q36A, B, C, E

Q37B

Q3812.22 to 12.28

Q39175

Q40175

Q4170

Q42C

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