# What do the percentiles mean in MSAR?

#### mariposas905

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What does it mean to be 10th, 25th or 90th percentile in the MCAT range according to MSAR? If the 10th percentile for a school is 507, does that mean 10% of its accepted students had 507 or below? Or is that the minimum score that school accepted?

And wouldn't the median score be skewed by high test scorers? Why do schools report the median instead of the mean (average)?

#### Yhorm the Giant

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you were right on your first guess.

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#### Goro

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What does it mean to be 10th, 25th or 90th percentile in the MCAT range according to MSAR? If the 10th percentile for a school is 507, does that mean 10% of its accepted students had 507 or below? Or is that the minimum score that school accepted?

And wouldn't the median score be skewed by high test scorers? Why do schools report the median instead of the mean (average)?
Take Biostats, well, stat.

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#### DBC03

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What does it mean to be 10th, 25th or 90th percentile in the MCAT range according to MSAR? If the 10th percentile for a school is 507, does that mean 10% of its accepted students had 507 or below? Or is that the minimum score that school accepted?

And wouldn't the median score be skewed by high test scorers? Why do schools report the median instead of the mean (average)?

I have wondered about this as well. I think the *mean* would be skewed by higher or lower scorers. But I could be misunderstanding your question. The median is just showing the number that shows up in the middle of all of the scores. I thought through this at the beginning of the application cycle and I appreciate using the median because then I know that half of the people have scored at or above the median value and half have scored at or below. If they use average, the number could be skewed from some serious outliers (for example, the lowest MCAT accepted by Duke was 498 and lowest GPA Accepted by Vanderbilt was a 3.1 last year - add that in to the rest of the stats and find the mean and then you have lower numbers that might not be representative of the GPA/MCAT needed to be a successful applicant).

I'm unfortunately below the 10% GPA threshold for most schools, so that does not inspire confidence.

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#### efle

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Means/averages are much more susceptible to skew than medians or IQRs

I'd read the wiki page real quick on percentiles. A 10th percentile of 50x does not mean that was the minimum admitted, but it does mean only 10% of admits were that low or lower.

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#### mariposas905

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Means/averages are much more susceptible to skew than medians or IQRs

I'd read the wiki page real quick on percentiles. A 10th percentile of 50x does not mean that was the minimum admitted, but it does mean only 10% of admits were that low or lower.

Hmm...so then 90th percentile would also mean that 10% of the applicants scored the 90th percentile score (517) or higher? I'm sure it can't mean that 90% of those applicants scored that score

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#### efle

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Hmm...so then 90th percentile would also mean that 10% of the applicants scored the 90th percentile score (517) or higher? I'm sure it can't mean that 90% of those applicants scored that score
Percentiles are always defined by the amount below/to the left in the curve. So 90th percentile means 90% scored that low or lower. (100 - percentile) gives you the amount doing better. So for example if 90th was a 517, then only 10% had a 517+. Or an alternative way to think about it, "98th percentile" means the same thing as "top 2%"

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#### hurtem&healem

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Or an alternative way to think about it, "98th percentile" means the same thing as "top 2%"
To be pedantic, 98th percentile is top 3%.

#### P0ke

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To be pedantic, 98th percentile is top 3%.
No it isn't. It's the top 2%

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#### efle

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To be pedantic, 98th percentile is top 3%.
Top 2.5% in AAMC metrics, if you really want to get pedantic (from 97.50 up to 100.0 is listed 98th-100th)

#### Inspired Chaos

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Isn't stats a requirement for basically every degree? So people understand percentiles and when/why medians are used? These skills are very important for digesting research if nothing else.

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#### wysdoc

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Top 2.5% in AAMC metrics, if you really want to get pedantic (from 97.50 up to 100.0 is listed 98th-100th)
For all the newbies, @efle is the go-to person for statistics here on SDN. Always a great explanation, thanks efle!

#### hurtem&healem

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No it isn't. It's the top 2%
98th percentile is AS GOOD AS or better than 98%. 98, 99, 100. The 100th percentile is the top 1%. What am I missing here?

#### Matthew9Thirtyfive

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98th percentile is AS GOOD AS or better than 98%. 98, 99, 100. The 100th percentile is the top 1%. What am I missing here?

There's no 100th percentile. That's just an approximation. The 99th is the top 1%. You'd be outscoring yourself if you were in the 100th percentile.

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#### SuaveCardigans

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There's no 100th percentile. That's just an approximation. The 99th is the top 1%. You'd be outscoring yourself if you were in the 100th percentile.
No, 528 is true 100th percentile because you are equal to or higher than everyone

#### Inspired Chaos

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See the way percentiles work is that out of every 100 people, you would be higher than ___ many of them. Can't be at the 100th or else it would have to be out of 101. So the 97th %ile means that out of every 100 people who took the test, you scored higher than 97 of them. Putting you in the top 3%.

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#### hurtem&healem

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See the way percentiles work is that out of every 100 people, you would be higher than ___ many of them. Can't be higher than 100 or else it would have to be out of 101. So the 97th %ile means that out of every 100 people who took the test, you scored higher than 97 of them. Putting you in the top 3%.
idk about anywhere else, but that's not how MCAT percentile work. 97th percentile is EQUAL TO or better than 97% of test takers. Hence, if you look at their percentile rankings, they have a 100th percentile.

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#### DBC03

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I thought the 100th %ile was actually 99.5+, so it's just an approximation, but it could be, say, 99.9% for 528. I can't remember where I read something along these lines, so someone correct me if I'm wrong.

#### P0ke

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idk about anywhere else, but that's not how MCAT percentile work. 97th percentile is EQUAL TO or better than 97% of test takers. Hence, if you look at their percentile rankings, they have a 100th percentile.
In the strict mathematical definition of percentile, 100th percentile would be impossible. You would need an infinitely large set of students for there to be a true 100th percentile. But as efle pointed out, the AAMC rounds up to the nearest integer, so the 99.5th percentile and up is reported as the 100th percentile. That's why there are 100th percentile scores reported.

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#### Inspired Chaos

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It depends on your language. You could score at the 99th %ile or in it. 99% of people score in it, only 1% scores at it. The only use for a 100th percentile is when talking about what figure is inclusive of all the data. For the MCAT, or any other exam, you cannot score at the 100th percentile. Everyone score within it.

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#### hurtem&healem

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It depends on your language. You could score at the 99th %ile or in it. 99% of people score in it, only 1% scores at it. The only use for a 100th percentile is when talking about what figure is inclusive of all the data. For the MCAT, or any other exam, you cannot score at the 100th percentile. Everyone score within it.
If you score a perfect 528, you are equal to or better than every single test taker. No rounding necessary. Again, I don't remember the convention elsewhere, but this is the language used in explaining the MCAT percentiles.

I'm not fixated on being right here, but everyone is responding talking about just being better than x% of test takers. The MCAT percentile is described as being EQUAL TO or better than x%, and nobody has explained how that excludes the possibility of a 100th percentile.

#### gonnif

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It depends on your language. You could score at the 99th %ile or in it. 99% of people score in it, only 1% scores at it. The only use for a 100th percentile is when talking about what figure is inclusive of all the data. For the MCAT, or any other exam, you cannot score at the 100th percentile. Everyone score within it.

I think, perhaps, the confusion is, that the MCAT, unlike most other exams I have seen, aggregates their data on a 1%-100% rank, instead of the typical 0%-99% . As @efle , the stats man here on SDN has pointed out you cant have more than 100% of anything (hopefully everyone knew that). Therefore, if you are in the top 1% of something, you have to be in the 99%-100% band or the 99th percentile

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#### Inspired Chaos

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If you score a perfect 528, you are equal to or better than every single test taker. No rounding necessary. Again, I don't remember the convention elsewhere, but this is the language used in explaining the MCAT percentiles.

I'm not fixated on being right here, but everyone is responding talking about just being better than x% of test takers. The MCAT percentile is described as being EQUAL TO or better than x%, and nobody has explained how that excludes the possibility of a 100th percentile.
I didn't realize that. I'm not sure what's going on here. I may be wrong, but my degree is in statistics and it's been hammered in my head that that language is incorrect.

This is how I learned:

https://magoosh.com/gre/2012/gre-math-percentiles-and-quartiles/

#### P0ke

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I think part of the confusion here is the MSAR uses percentile, whereas MCAT scores are reported as percentile ranks.
The formula for percentile ranks is: FORMULA
Where cl is the count of scores less than the score of interest, fi is the frequency of scores of interest, and N is the number of examinees. This formula implies that a 100th percentile rank is impossible. For example, out of 100 students, if 1 student scores a perfect 100, then the percentile rank would be (99 + 0.5*1)/100 = 99.5%

The percentile rank is the percentage of scores below or equal to a given score, as hurtem was alluding to, but it takes the midpoint of the frequency of the scores at the given score. This is demonstrable with the following image from Definition of Percentile Rank

IMAGE

Notice that the percentile rank for "B" is 77 and not 92, because it takes the midpoint of the B scores. So a true 100th percentile rank should still be impossible, but my guess is that they still round these scores up as efle stated.

edit: the pics weren't showing up so I put links to them

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#### Matthew9Thirtyfive

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No, 528 is true 100th percentile because you are equal to or higher than everyone

That's not how percentiles work. You cannot score higher than 100% of the people. That includes yourself. You cannot score higher than yourself. They write 100 as an approximation.

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#### Matthew9Thirtyfive

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I think, perhaps, the confusion is, that the MCAT, unlike most other exams I have seen, aggregates their data on a 1%-100% rank, instead of the typical 0%-99% . As @efle , the stats man here on SDN has pointed out you cant have more than 100% of anything (hopefully everyone knew that). Therefore, if you are in the top 1% of something, you have to be in the 99%-100% band or the 99th percentile

View attachment 222777

Right. There's no such thing as a 100th percentile, but they can approximate or use percentage bands (which is what they do).

#### efle

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To make things even more confusing, the MCAT until a couple years ago used to report the full percentile bin and not just the ceiling, so you could have a score shown as "97.6 - 98.4" and the highest scores were shown as percentile range "99.9 - 99.9"

Now they just round off and report the single upper bound value.

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#### hurtem&healem

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That's not how percentiles work. You cannot score higher than 100% of the people. That includes yourself. You cannot score higher than yourself. They write 100 as an approximation.
You keep saying the same thing while ignoring what is being pointed out. You by definition score the same as yourself and the MCAT percentile is reported as whom you scored equal to or better than. Not just just better than. Equal to. If 100 people take the test, and you scored best, you scored equal to or better than 100% of the test takers. That is what MCAT reports.

Edit: Allegedly. This is what they allegedly report. If you want to say they're wrong in explaining their own reporting, okay, I'll buy it.

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#### efle

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98th percentile is AS GOOD AS or better than 98%. 98, 99, 100. The 100th percentile is the top 1%. What am I missing here?
Think of what proportion qualifies for a better title. Say we only round to the tenth's place. If you are at 98.0, then 98.1-100 is above you. That means 1.9% is above you. So you sit on the bottom margin of the "top 2%".

I suppose you could also think of it in terms of other divisions, like quartiles. If I say I sit at the margin of the first quartile, that means exactly 25% are the same or lower. Can't be 24% or 26%, because then four quartiles wouldn't sum to 100.

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#### SuaveCardigans

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That's not how percentiles work. You cannot score higher than 100% of the people. That includes yourself. You cannot score higher than yourself. They write 100 as an approximation.
From How is the MCAT Scored? under the section titled "Understanding percentile ranks":
The percentile ranks provided on your score report show the percentages of test takers who received the same scores or lower scores on the exam than you did. They show how your scores compare to the scores of other examinees.

I am not trying to debate the true meaning of percentile, but just explain how the AAMC considers its reporting. Based on their definition, a 528 is a true 100th percentile score, and not rounded up to 100. If you disagree with that definition, take it up with the AAMC.

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#### P0ke

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You keep saying the same thing while ignoring what is being pointed out. You by definition score the same as yourself and the MCAT percentile is reported as whom you scored equal to or better than. Not just just better than. Equal to. If 100 people take the test, and you scored best, you scored equal to or better than 100% of the test takers. That is what MCAT reports.

Edit: Allegedly. This is what they allegedly report. If you want to say they're wrong in explaining their own reporting, okay, I'll buy it.

I explained why this is wrong in my example above. Yes, percentile rank does take scores at the same score into account, but it takes the midpoint of the distribution at that score, not the highest point. If 1 student out of 100 scores a perfect score, his/her percentile rank is 99.5.

I think part of the confusion here is the MSAR uses percentile, whereas MCAT scores are reported as percentile ranks.
The formula for percentile ranks is: FORMULA
Where cl is the count of scores less than the score of interest, fi is the frequency of scores of interest, and N is the number of examinees. This formula implies that a 100th percentile rank is impossible. For example, out of 100 students, if 1 student scores a perfect 100, then the percentile rank would be (99 + 0.5*1)/100 = 99.5%

The percentile rank is the percentage of scores below or equal to a given score, as hurtem was alluding to, but it takes the midpoint of the frequency of the scores at the given score. This is demonstrable with the following image from Definition of Percentile Rank

IMAGE

Notice that the percentile rank for "B" is 77 and not 92, because it takes the midpoint of the B scores. So a true 100th percentile rank should still be impossible, but my guess is that they still round these scores up as efle stated.

edit: the pics weren't showing up so I put links to them
From How is the MCAT Scored? under the section titled "Understanding percentile ranks":
The percentile ranks provided on your score report show the percentages of test takers who received the same scores or lower scores on the exam than you did. They show how your scores compare to the scores of other examinees.

I am not trying to debate the true meaning of percentile, but just explain how the AAMC considers its reporting. Based on their definition, a 528 is a true 100th percentile score, and not rounded up to 100. If you disagree with that definition, then frankly my dear I dont give a damn and take it up with the AAMC.

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#### Lawpy

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Are we discussing MSAR percentiles, MCAT percentiles or general definition of percentiles?

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#### Matthew9Thirtyfive

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You keep saying the same thing while ignoring what is being pointed out. You by definition score the same as yourself and the MCAT percentile is reported as whom you scored equal to or better than. Not just just better than. Equal to. If 100 people take the test, and you scored best, you scored equal to or better than 100% of the test takers. That is what MCAT reports.

Edit: Allegedly. This is what they allegedly report. If you want to say they're wrong in explaining their own reporting, okay, I'll buy it.

And you continue to ignorantly "correct" me without understanding how percentiles work. As gonnif said, there is a difference between a percent band and a percentile. You can be in the 100% band. You cannot be in the 100 percentile.

The percentile rank is ten percent of scores at or below your score. You cannot equal 100%, because even if everyone is below your score, you still have your own score which cannot be below or at anything else.

The formula is the count of all scores less than the score of interest plus one half the frequency of that score all over the total population times 100. You can get extremely close to 100%, but you can't get there. At 99.99 they just round up.

#### SuaveCardigans

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Are we discussing MSAR percentiles, MCAT percentiles or general definition of percentiles?
It seems to be all 3, which is why this is going downhill

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#### efle

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And you continue to ignorantly "correct" me without understanding how percentiles work. As gonnif said, there is a difference between a percent band and a percentile. You can be in the 100% band. You cannot be in the 100 percentile.

The percentile rank is ten percent of scores at or below your score. You cannot equal 100%, because even if everyone is below your score, you still have your own score which cannot be below or at anything else.

The formula is the count of all scores less than the score of interest plus one half the frequency of that score all over the total population times 100. You can get extremely close to 100%, but you can't get there. At 99.99 they just round up.
Isn't that the exclusive way of using percentile though? Whereas inclusive would allow for 100th percentile scores. I think you guys are arguing past each other about this, most of the time percentiles are used exclusively but the AAMC for whatever reason uses them inclusively.

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#### Lawpy

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Isn't that the exclusive way of using percentile though? Whereas inclusive would allow for 100th percentile scores. I think you guys are arguing past each other about this, most of the time percentiles are used exclusively but the AAMC for whatever reason uses them inclusively.

I think this is the best compromise to resolve the impasse.

#### P0ke

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Are we discussing MSAR percentiles, MCAT percentiles or general definition of percentiles?
MSAR reports percentiles, MCAT scores are given percentile ranks
Isn't that the exclusive way of using percentile though? Whereas inclusive would allow for 100th percentile scores. I think you guys are arguing past each other about this, most of the time percentiles are used exclusively but the AAMC for whatever reason uses them inclusively.
Look at the wording of what gonnif posted. MCAT uses percentile rank, which has a different definition from percentile.

#### efle

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Look at the wording of what gonnif posted. MCAT uses percentile rank, which has a different definition from percentile.
Well, strictly speaking the formula for percentile rank is:

Where C is scores lower and F is scores equivalent. This formula cannot output a true 100.00 value, yet just looking at the language (all scores equal or lower) you'd say a 528 is true 100.00 percentile.

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#### P0ke

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Well, strictly speaking the formula for percentile rank is:

Where C is scores lower and F is scores equivalent. This formula cannot output a true 100.00 value, yet just looking at the language (all scores equal or lower) you'd say a 528 is true 100.00 percentile.
I explained this all in my post above, with that exact image and more...

I think part of the confusion here is the MSAR uses percentile, whereas MCAT scores are reported as percentile ranks.
The formula for percentile ranks is: FORMULA
Where cl is the count of scores less than the score of interest, fi is the frequency of scores of interest, and N is the number of examinees. This formula implies that a 100th percentile rank is impossible. For example, out of 100 students, if 1 student scores a perfect 100, then the percentile rank would be (99 + 0.5*1)/100 = 99.5%

The percentile rank is the percentage of scores below or equal to a given score, as hurtem was alluding to, but it takes the midpoint of the frequency of the scores at the given score. This is demonstrable with the following image from Definition of Percentile Rank

IMAGE

Notice that the percentile rank for "B" is 77 and not 92, because it takes the midpoint of the B scores. So a true 100th percentile rank should still be impossible, but my guess is that they still round these scores up as efle stated.

edit: the pics weren't showing up so I put links to them

#### P0ke

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Well, strictly speaking the formula for percentile rank is:

Where C is scores lower and F is scores equivalent. This formula cannot output a true 100.00 value, yet just looking at the language (all scores equal or lower) you'd say a 528 is true 100.00 percentile.
Percentile rank does explain how you did in relation to people with equal or worse scores, but it assumes you are at the midpoint of the distribution of people with the same score, since you can't say you got the best possible version of that score, or the worst possible version of that score. Even if you are the sole person who scores a 528, it puts your percentile rank at the midpoint of the 528 distribution. It might be used to compensate for having discrete scores instead of continuous scores (i.e. There's no 527.74748 vs 527.5364747, so it just puts you at the midpoint of that discrete score's distribution)

#### efle

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I explained this all in my post above, with that exact image and more...
Percentile rank does explain how you did in relation to people with equal or worse scores, but it assumes you are at the midpoint of the distribution of people with the same score, since you can't say you got the best possible version of that score, or the worst possible version of that score. Even if you are the sole person who scores a 528, it puts your percentile rank at the midpoint of the 528 distribution. It might be used to compensate for having discrete scores instead of continuous scores (i.e. There's no 527.74748 vs 527.5364747, so it just puts you at the midpoint of that discrete score's distribution)
Sorry, haven't been keeping up with the thread very closely.

The bolded weirds me out. I don't understand why the formula isn't [C + f] / N if you're using a discrete scaled score system like the MCAT. It isn't really possible to have one 33 be higher/lower than another 33 when the subsections have different values per point (like how many Verbal questions is equal to one Physics question? Does that make 10/12/11 better than 12/10/11 etc)

#### P0ke

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Sorry, haven't been keeping up with the thread very closely.

The bolded weirds me out. I don't understand why the formula isn't [C + f] / N if you're using a discrete scaled score system like the MCAT. It isn't really possible to have one 33 be higher/lower than another 33 when the subsections have different values per point (like how many Verbal questions is equal to one Physics question? Does that make 10/12/11 better than 12/10/11 etc)
If you have a group of people who all got 33s, who got the best 33? There's no way to distinguish them. So everyone is put at the middle of the distribution of 33s when comparing their scores to other scores. Neither of those scores is better than another when comparing aggregate scores, that's the point.
If half of test takers got a perfect score, you can't just say they're all the best. You can only say that they're at the 75th percentile rank because thats the midpoint of the perfect score distribution (50-100th percentile)

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#### DBC03

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If you have a group of people who all got 33s, who got the best 33? There's no way to distinguish them. So everyone is put at the middle of the distribution of 33s when comparing their scores to other scores. Neither of those scores is better than another when comparing aggregate scores, that's the point.

Well, technically with the new MCAT, you could have scored, say, in the 90th percentile with a 128 in CARS, but only in the 86th percentile with a 128 in Psych/Soc. So in this case, a combined score with a 128 in CARS might be in a slightly higher percentile than someone with the same combined score and a 128 in Psych/Soc.

#### P0ke

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Well, technically with the new MCAT, you could have scored, say, in the 90th percentile with a 128 in CARS, but only in the 86th percentile with a 128 in Psych/Soc. So in this case, a combined score with a 128 in CARS might be in a slightly higher percentile than someone with the same combined score and a 128 in Psych/Soc.
I was talking about purely aggregate score. Of course adcoms are free to interpret individual scores however they like, but there's no objective way to compare individual score distributions, with the same aggregate score.

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#### DBC03

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I was talking about purely aggregate score. Of course adcoms are free to interpret individual scores however they like, but there's no objective way to compare individual score distributions, with the same aggregate score.

Agreed.

Sent from my iPhone using SDN mobile

#### efle

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If half of test takers got a perfect score, you can't just say they're all the best. You can only say that they're at the 75th percentile rank because thats the midpoint of the perfect score distribution (50-100th percentile)
And this is what makes the description "equal or lower" bizarre to me. If half the takers make zero errors - not just a perfect scaled score but literally zero errors - then they were above 50% of testers and exactly equal to another 50% of testers. So what's the sum of the two? 75% ?!?!

Really the description is "half of those equal, and all of those lower"

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#### P0ke

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Sorry, haven't been keeping up with the thread very closely.

The bolded weirds me out. I don't understand why the formula isn't [C + f] / N if you're using a discrete scaled score system like the MCAT. It isn't really possible to have one 33 be higher/lower than another 33 when the subsections have different values per point (like how many Verbal questions is equal to one Physics question? Does that make 10/12/11 better than 12/10/11 etc)
As a more concrete example, the old GRE used to have subsections scored 200-800.
A perfect score (800) on the old GRE math subsection was a 91 percentile rank
Then they made a new test, which was more able to distinguish really good math students from really great math students, and a perfect score on the new GRE is the 97th percentile rank.
So percentile rank does exactly what its name implies, it ranks you against other people who have taken the test.

Lets say you're the only person who took a test and got a perfect score on it. You're at the 100th percentile... Congratulations! (*clap* *clap* *clap*). But this tells you nothing about how you've fared against other people, which percentile rank does (you're at the 50th percentile rank)

Now lets say you take a super hard test, and you're the only perfect score out of 1,000,000 people who have taken it. Again, you're at the 100th percentile... But this time, you're at the 99.99995th percentile rank... Now this tells more of a story of how many asses you've had to kick to stay at the top of the mountain, whereas percentile does not. With each person succumbing to the test with a less than perfect score, your percentile rank goes up and up. Also, it can show the tests difficulty, as shown with the GRE example. In general it just gives more information.

These are all just my hypotheses for why percentile rank is used... All I know for sure is the definition.

#### efle

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See now this gets even weirder for me, because if you just want to know how you compare to others, you can just use the lower bound. If a full 10% get a perfect score, report them all as 90th percentile so it is easy to see that 10% of other people out there are just as awesome. When all I see is 95th percentile for that situation, it's not doing a good job whatsoever of communicating how rare a perfect score is.

#### hurtem&healem

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And we wonder why the general public has a distrust statistics...