Not even sure if I should expose my ignorance (or that of others) here. But this question has been bugging me for a few years now. And I don't see any street protests by mathematicians anywhere. So may be I am wrong. But let me get the bug out of my system anyway.
A percentile is a great invention, by someone who wanted to compare people. As scales go, it is supposed to measure things on an ordinal, or comparative, scale. By definition, it is the number of people below you, if your percentile score is being discussed. If I have a 75 percentile, it should mean that 75% of the students who took the exam with me are below my score (whatever the raw score- that could be 5, or 50, or even 0, if negative marking is allowed, coz some would score minus marks in such a scenario).
Now, a percentile score of 100 is an impossibility by this definition. Because you are one of the people who make up the 100% of the test-taking population. Therefore, you necessarily have to exclude yourself while stating your percentile score- if 100% of the people were below your score, then who are you (only in a limited, not an existential, sense) ?
I have a major problem here. Hope the CATs of tis world and the reporters (don't know if they have a stats course) will solve this riddle for me.
Meoww!
A percentile is a great invention, by someone who wanted to compare people. As scales go, it is supposed to measure things on an ordinal, or comparative, scale. By definition, it is the number of people below you, if your percentile score is being discussed. If I have a 75 percentile, it should mean that 75% of the students who took the exam with me are below my score (whatever the raw score- that could be 5, or 50, or even 0, if negative marking is allowed, coz some would score minus marks in such a scenario).
Now, a percentile score of 100 is an impossibility by this definition. Because you are one of the people who make up the 100% of the test-taking population. Therefore, you necessarily have to exclude yourself while stating your percentile score- if 100% of the people were below your score, then who are you (only in a limited, not an existential, sense) ?
I have a major problem here. Hope the CATs of tis world and the reporters (don't know if they have a stats course) will solve this riddle for me.
Meoww!
3 comments:
According to the concept of duality - regardless of 'percentile' if you are 'person' standing on the 'tile' you could still be on the ceiling (For the fella below you). Are you floored oh mortal!
Yes, a percentile score of 100 on a test is not possible. Does CAT give a 100 as a percentile score to students?
For a large enough number of test takers, though, one could get very close to 100. Say 99.99999th percentile. Perhaps at some point they decide to round up and say that the percentile score is 100 for all practical purposes, even though technically incorrect.
Not only do they give it, but every newspaper announces how many got a 100 percentile. It's infantile, but probably rounding it off without telling anyone.
DH, thanks for letting me know where I stand- on a tile!
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