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If it’s talking about matriculant GPA, a 10th percentile of 506 means that 10% of the matriculants had MCAT scores below 506.
 
In the MSAR we see the ranges of GPA and MCAT scores from the 10th to 90th percentile. This might be a stupid question, BUT... i'm gonna ask it anyway.

If a school's 10th percentile for MCAT is 506, does that mean that that was the cut-off? or do they accept a few students with 504 or 505, given that 506 is in the 10th percentile?

Not a troll. I am seriously asking. Thanks!
It might be a good idea to take a stats course.
 
If a school matriculated 200 students and has a 10th percentile of 505, that means 20 students had below a 505.
It could also mean than it has a cut off of 505 and 21 students (or more) had 505.
 
I think it specifically means below 505 so 21 had 504 or less.

If we took all the matriculants' MCAT scores and put them in rank order and lopped off the bottom 10% what MCAT score would be at that 10th percentile?

Now let's say that there is a hard 505 cut off and, in fact, 30 of the 200 matriculants had a MCAT of 505 and no one had a score lower than 505. The 10th percentle would be 505.

Just for giggles we could say that 30 had a score of 505 and 2 had a score of 504. The 10th percentile of 505 still means that the bottom 10% of the class had a MCAT of 505 or lower, not 504 or lower.
 
Did a little googling. Looks like the strict definition of percentile is greater than x%, as opposed to greater than or equal to. If a class of 200 had a hard cutoff at 505 and 30 people with a 505, most stats software should report 505 as percentile: 0, because none of the set falls below 505.

AAMC used to be good about this, reporting MCAT score percentiles as intervals and capping the highest reported value at 99.9-99.9, since 100.oth isn't strictly possible. They've since abandoned this, or else just changed software or something, and now report the upper bound including 100th. So what they give you isn't the traditional percentile any more.

Whether the software generating the MSAR boxplots uses strict definition of percentile is anyone's guess. It might just start counting from the bottom and report the value after reaching student #21 in the class of 200, as if finding a median.
 
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