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The qualifying marks for an exam attempted by a large number of students are set at half of the median of the marks scored in that exam. Under this condition, 10% of the candidates fail. If the qualifying marks are set at the median of the scores, and if no two students have the same marks, the percentage of candidates failing will be closest to
- a)20%
- b)25%
- c)33%
- d)50%
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The qualifying marks for an exam attempted by a large number of studen...
Case 1: Consider 100 students attempting the exam and the exam is of 100 marks.
- Now it is given that no two students have the same marks. Each student will have a different score.
- So, if the median of the marks achieved is considered, it will be : X = (49+50)/2 = 49.5
- Now, in this case, the cut-off is half of the median: X/2 = 25.25
- Here, 90 students pass and 10 fail.
Case 2: Now, here the median is double of case 1: X = 49.5.
- As it is given that no students can have the same score. So, the students scoring from 50 to 100 have passed the exam.
- So, in total 51 students passed the exam.
- Out of 100,51 students clear the exam which states that approx 50% of students failed the exam.
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The qualifying marks for an exam attempted by a large number of studen...
Qualifying Marks at Half of the Median
- In this scenario, the qualifying marks are set at half of the median of the marks scored in the exam.
- This means that 50% of the students score above the qualifying marks and 50% score below.
- Therefore, the passing percentage is 50%.
Qualifying Marks at the Median
- When the qualifying marks are set at the median of the scores, the passing percentage changes.
- Since no two students have the same marks, the median will be the score of the middle student.
- In this case, 50% of the students will score below the median and 50% will score above.
- Therefore, the passing percentage is 50%.
- Since the passing percentage is closest to 50%, the answer is option 'D'.
- In this scenario, the qualifying marks are set at half of the median of the marks scored in the exam.
- This means that 50% of the students score above the qualifying marks and 50% score below.
- Therefore, the passing percentage is 50%.
Qualifying Marks at the Median
- When the qualifying marks are set at the median of the scores, the passing percentage changes.
- Since no two students have the same marks, the median will be the score of the middle student.
- In this case, 50% of the students will score below the median and 50% will score above.
- Therefore, the passing percentage is 50%.
- Since the passing percentage is closest to 50%, the answer is option 'D'.
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The qualifying marks for an exam attempted by a large number of students are set at half of the median of the marks scored in that exam. Under this condition, 10% of the candidates fail. If the qualifying marks are set at the median of the scores, and if no two students have the same marks, the percentage of candidates failing will be closest toa)20%b)25%c)33%d)50%Correct answer is option 'D'. Can you explain this answer?
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