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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
- a)is decreased by 2
- b)is two times the original median
- c)remains the same as that of the original set
- d)is increased by 2
Correct answer is option 'C'. Can you explain this answer?
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The median of a set of 9 distinct observations is 20.5. If each of the...
Question Analysis:
We are given a set of 9 distinct observations and their median is 20.5. We need to determine what happens to the median if we increase the largest 4 observations by 2.
Given Information:
- Set of 9 distinct observations
- Median of the original set is 20.5
- Largest 4 observations are increased by 2
Solution:
To solve this problem, let's consider the possible scenarios and analyze their effects on the median.
Scenario 1: The median is one of the largest 4 observations
If the median is one of the largest 4 observations, increasing the largest 4 observations by 2 will also increase the median by 2. In this case, the median of the new set will be 20.5+2=22.5, which is not equal to the original median. Hence, this scenario is not possible.
Scenario 2: The median is the smallest observation among the largest 5
If the median is the smallest observation among the largest 5, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
Scenario 3: The median is the largest observation among the smallest 4
If the median is the largest observation among the smallest 4, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
Scenario 4: The median is one of the smallest 4 observations
If the median is one of the smallest 4 observations, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
From the analysis of all possible scenarios, we can conclude that the median of the new set remains the same as that of the original set. Therefore, the correct answer is option 'C'.
We are given a set of 9 distinct observations and their median is 20.5. We need to determine what happens to the median if we increase the largest 4 observations by 2.
Given Information:
- Set of 9 distinct observations
- Median of the original set is 20.5
- Largest 4 observations are increased by 2
Solution:
To solve this problem, let's consider the possible scenarios and analyze their effects on the median.
Scenario 1: The median is one of the largest 4 observations
If the median is one of the largest 4 observations, increasing the largest 4 observations by 2 will also increase the median by 2. In this case, the median of the new set will be 20.5+2=22.5, which is not equal to the original median. Hence, this scenario is not possible.
Scenario 2: The median is the smallest observation among the largest 5
If the median is the smallest observation among the largest 5, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
Scenario 3: The median is the largest observation among the smallest 4
If the median is the largest observation among the smallest 4, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
Scenario 4: The median is one of the smallest 4 observations
If the median is one of the smallest 4 observations, increasing the largest 4 observations by 2 will not affect the median. In this case, the median of the new set will remain the same as the original median, which is 20.5.
From the analysis of all possible scenarios, we can conclude that the median of the new set remains the same as that of the original set. Therefore, the correct answer is option 'C'.
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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer?
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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer?.
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer?.
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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new seta)is decreased by 2b)is two times the original medianc)remains the same as that of the original setd)is increased by 2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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