# usmle score mean vs. median score

#### globulin

##### Member
15+ Year Member
Hey, I've heard the score report says the MEAN is 215 and the standard deviation is 21. But you can't really correlate that to a percentile rank, can you? Don't you need the median score to do that? So if someone scores a 236, that doesn't necessarily mean they're percentile rank is 68% which is 1 SD. right? Because the mean could be higher or lower than the median. Anyway, so do they give a median score or what? Thanks.

#### globulin

##### Member
15+ Year Member
I was rethinking my previous post. I guess if the mean is 215 and the SD is 21. Then that means 68% of people fall between 194 and 236. Which then means that 32% would either be below 194 or above 236 which means that 16% would be higher than 236 which correlates to 84% percentile. however, then I was thinking, that should only work with median scores, right? It can't work with mean scores because theoretically you could have 9 people getting a score of say 250 and higher and one person getting a score of 10. So that person who got a 10 would lower the mean even though almost everyone got higher than the mean. So basically what I guess I'm trying to get at is am i right or what in that you can't figure out your percentile score with just the mean and SD? And if I am, does the USMLE give you the median score so you can figure it out? I'm so not articulate and can't explain myself and this post is too analytical and dorky. I apologize if your cerebrum exploded while reading this.

#### TXSPE

##### Junior Member
15+ Year Member
Globulin- I think you are correct in that you can approximately figure out your percentile rank with mean and SD. Assuming you beat the mean by one SD, then yes you would roughly be in the 85% percentile. This is assuming a normal distribution (not skewed) because if it is a normal distribution mean=median=mode. The mean changes every year, and according to the USMLE website it is usually between 200-220, with most scores between 160-240. If this is correct than a mean of 215 is not a normal distribution (it is positively skewed). Unfortunately, in 1999 NBME stopped reporting percentile scores because of differences in ranges of scores among different examination dates. I hope this helps

15+ Year Member

#### southerndoc

##### life is good
Volunteer Staff
15+ Year Member
Remember, means and SD's are only estimates of central tendency. You can only get an approximate percentile and never an exact one.

However, keep in mind that the scenario you describe (a lot of high scores and one score at 10) would create a smaller standard deviation.

The mean and the standard deviation will give you a good approximation of your rank. Are you familiar with Z tables? If so, then you can figure out your exact percentile approximation (e.g., instead of just saying that you're in the top 16%, you could use a Z table to find that you are in the top 11%, etc.).

#### Kluver Bucy

##### Gold Member
15+ Year Member
Who says the USMLE has a normal distribution? If you had a group take an IQ test, took the top 2% of those and had them take another IQ test, you'd expect a similar distribution: a wedge. Granted, med student selection and USMLE scores aren't direct measures of intelligence, but they're not random samples of the general population either.

•••quote:•••Originally posted by gims:

#### globulin

##### Member
15+ Year Member

•••quote:•••Originally posted by TXSPE:
•Globulin- I think you are correct in that you can approximately figure out your percentile rank with mean and SD. Assuming you beat the mean by one SD, then yes you would roughly be in the 85% percentile. This is assuming a normal distribution (not skewed) because if it is a normal distribution mean=median=mode. The mean changes every year, and according to the USMLE website it is usually between 200-220, with most scores between 160-240. If this is correct than a mean of 215 is not a normal distribution (it is positively skewed). Unfortunately, in 1999 NBME stopped reporting percentile scores because of differences in ranges of scores among different examination dates. I hope this helps•••••

#### Grohaila

##### Junior Member
7+ Year Member
15+ Year Member
•••quote:•••Originally posted by Kluver Bucy:
• If you had a group take an IQ test, took the top 2% of those and had them take another IQ test, you'd expect a similar distribution: a wedge. •••••Of course, that's assuming no variability within tests (an individual doing poorer or better due to fatigue or luck) and between tests (folks improving their test-taking proficiency to different degrees and tests being different in themselves).

All things considered, your wedge would be smoothed out towards a gaussian...

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