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Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
- a)P, Q
- b)Q, R
- c)P, R
- d)R, S
Correct answer is option 'C'. Can you explain this answer?
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Which of the following assertions are CORRECT?P: Adding 7 to each entr...
P and R always hold true
Else consider a sample set {1, 2, 3, 4} and check accordingly
Else consider a sample set {1, 2, 3, 4} and check accordingly
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Which of the following assertions are CORRECT?P: Adding 7 to each entr...
Correct Assertions Regarding Effects of Adding and Doubling Entries in a List
The following assertions are correct:
- Adding 7 to each entry in a list adds 7 to the mean of the list (P)
- Adding 7 to each entry in a list does not add 7 to the standard deviation of the list (not Q)
- Doubling each entry in a list doubles the mean of the list (R)
- Doubling each entry in a list does not leave the standard deviation of the list unchanged (not S)
Explanation:
Adding a constant value to each entry in a list affects the measures of central tendency (mean, median, mode) but not the measures of dispersion (standard deviation, range, quartiles), as they are based on the differences between the values and the mean.
- Adding 7 to each entry in a list adds 7 to the sum of the list, and thus increases the mean of the list by 7. For example, if a list has entries [1, 3, 5], the mean is (1+3+5)/3 = 3, and adding 7 to each entry results in [8, 10, 12], with a new mean of (8+10+12)/3 = 10.
- Adding a constant value to each entry does not affect the differences between the entries, and thus does not affect the standard deviation of the list. For example, if a list has entries [1, 3, 5], the standard deviation is 1.63, and adding 7 to each entry results in [8, 10, 12], with the same standard deviation of 1.63.
- Doubling each entry in a list doubles the sum of the list, and thus doubles the mean of the list. For example, if a list has entries [1, 3, 5], the mean is 3, and doubling each entry results in [2, 6, 10], with a new mean of 6.
- Doubling each entry in a list affects the differences between the entries, and thus affects the standard deviation of the list. Doubling each entry multiplies the standard deviation by 2, as it amplifies the relative distances from the mean. For example, if a list has entries [1, 3, 5], the standard deviation is 1.63, and doubling each entry results in [2, 6, 10], with a new standard deviation of 3.27.
Therefore, the correct assertions are P and R, and the incorrect assertions are Q and S.
The following assertions are correct:
- Adding 7 to each entry in a list adds 7 to the mean of the list (P)
- Adding 7 to each entry in a list does not add 7 to the standard deviation of the list (not Q)
- Doubling each entry in a list doubles the mean of the list (R)
- Doubling each entry in a list does not leave the standard deviation of the list unchanged (not S)
Explanation:
Adding a constant value to each entry in a list affects the measures of central tendency (mean, median, mode) but not the measures of dispersion (standard deviation, range, quartiles), as they are based on the differences between the values and the mean.
- Adding 7 to each entry in a list adds 7 to the sum of the list, and thus increases the mean of the list by 7. For example, if a list has entries [1, 3, 5], the mean is (1+3+5)/3 = 3, and adding 7 to each entry results in [8, 10, 12], with a new mean of (8+10+12)/3 = 10.
- Adding a constant value to each entry does not affect the differences between the entries, and thus does not affect the standard deviation of the list. For example, if a list has entries [1, 3, 5], the standard deviation is 1.63, and adding 7 to each entry results in [8, 10, 12], with the same standard deviation of 1.63.
- Doubling each entry in a list doubles the sum of the list, and thus doubles the mean of the list. For example, if a list has entries [1, 3, 5], the mean is 3, and doubling each entry results in [2, 6, 10], with a new mean of 6.
- Doubling each entry in a list affects the differences between the entries, and thus affects the standard deviation of the list. Doubling each entry multiplies the standard deviation by 2, as it amplifies the relative distances from the mean. For example, if a list has entries [1, 3, 5], the standard deviation is 1.63, and doubling each entry results in [2, 6, 10], with a new standard deviation of 3.27.
Therefore, the correct assertions are P and R, and the incorrect assertions are Q and S.
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Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer?
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Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer?.
Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following assertions are CORRECT?P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the listS: Doubling each entry in a list leaves the standard deviation of the list unchangeda)P, Qb)Q, Rc)P, Rd)R, SCorrect answer is option 'C'. Can you explain this answer?.
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