The IIT Madras BS Statistics for Data Science I (Stats 1) Qualifier paper sat on 16 Mar 2025, in the January 2025 term: 17 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
An inspection officer wants to test the tensile strength of threaded rods produced by a factory. If the inspection officer is interested to test the tensile strength of threaded rods produced by the factory in different months of year 2022 and collected the data for the same, then choose the correct option:
It is time-series data.
It is cross-sectional data.
Correct answer
It is time-series data.
A survey is conducted to assess the monthly income of families in a town. Respondents are asked to select one of the following options:
• Less than Rs. 20000
• Rs. 20000 - Rs. 40000
• Rs. 40000 - Rs. 60000
• More than Rs. 60000
What kind of scale of measurement has been used here?
Ordinal
Interval
Ratio and interval
Both ordinal and interval
Correct answer
Ordinal
Choose the correct option:
If the large values of variable X tend to be associated with small values of variable Y, then the correlation between X and Y will be positive.
If the points are located densely in a scatter diagram, then we can always expect a poor correlation between the variables.
Correlation is a unitless measure of association.
Correlation always lie between 0 and 1.
Correct answer
Correlation is a unitless measure of association.
Choose the correct statement/s ?
A nominal scale has the property of labelling the categories and it does not involve the ranking of data.
An ordinal scale has all the properties of nominal scale and it involves the ranking of data.
An Interval scale has all the properties of ordinal scale and it satisfies the absolute zero property.
A ratio scale has all the properties of interval scale and it does not satisfy the absolute zero property.
Correct answers
A nominal scale has the property of labelling the categories and it does not involve the ranking of data.
An ordinal scale has all the properties of nominal scale and it involves the ranking of data.
Samiksha 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:
Median of the new data is same as of old data.
New data will be bimodal.
Median of the new data will change.
New data will be unimodal.
Correct answers
Median of the new data is same as of old data.
New data will be bimodal.
Correct answers
Figure Q.1 shows the pie chart representation of the weightage distribution of 5 different subjects in an exam.
If the exam is of 300 marks, then what is the aggregate marks in Physics and Biology?
Correct answer: 135
The sum of 12 observations is 60, and the sum of their squares is 360. Find the population standard deviation. Enter the answer correct to two decimal places.
Correct answer: 2.24 (accepted within ±0.03)
Correct answer: 10
Based on the above data, answer the given subquestions.
What is the relative frequency of respondents who prefer Public Transport? Enter the answer correct to one decimal place.
Correct answer: 0.3
Based on the above data, answer the given subquestions.
Which mode of transport has the lowest relative frequency?
Car
Bicycle
Public Transport
Bike
Correct answer
Car
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.
Identify the sample and the population.
The population is all the students at IIT Madras campus.
The sample is all the final year students at IIT Madras campus.
The sample is 100 randomly selected final year students at IIT Madras campus.
The population is all the final year students at IIT Madras campus.
Correct answers
The population is all the students at IIT Madras campus.
The sample is 100 randomly selected final year students at IIT Madras campus.
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.
Identify the correct statement from the following?
Selected sample is a good representation of the population
Selected sample is not a good representation of the population.
Correct answer
Selected sample is not a good representation of the population.
Based on the above data, answer the given subquestions.
What is the mean number of awards given to the drama club if each observation is multiplied by 2 after adding 3 to it?
Correct answer: 76
Based on the above data, answer the given subquestions.
What is the median number of awards given to the drama club ?
36
34
38
32
Correct answer
36
An analyst wants to check whether the number of hours a student spent in learning is related to their exam performance. She randomly selects 6 students from the top 15 students of the class and data for the same is tabulated in Table Q.2
Based on the given information, answer the subquestions.
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.
Correct answer: 0.047 (accepted within ±0.004)
An analyst wants to check whether the number of hours a student spent in learning is related to their exam performance. She randomly selects 6 students from the top 15 students of the class and data for the same is tabulated in Table Q.2
Based on the given information, answer the subquestions.
Are the exam results of the selected students strongly influenced by the number of hours spent studying?
Yes, because the absolute value of Point Bi-serial coefficient is close to 1.
No, because the absolute value of Point Bi-serial coefficient is close to 1.
Yes, because the absolute value of Point Bi-serial coefficient is close to 0.
No, because the absolute value of Point Bi-serial coefficient is close to 0.
Correct answer
No, because the absolute value of Point Bi-serial coefficient is close to 0.
