How average is "median"?

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usuaggie
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Re: How average is "median"?

Postby usuaggie » Thu Apr 28, 2011 6:47 pm

bdubs wrote:
TaipeiMort wrote:Some years/schools the top 10% may be the same people in every class, some schools they may be completely dispersed. For example, at uChicago the "median" grade is a 177 (B), and top-ten percent at graduation is a 179.5, which is a B+, a top 5% is something like 180.5.

I would guess the distribution is something like:

C+,B-,B-(close to median),B,B,B,B,B,B+,A

this would mean that 80% are close to median or above.


Thank you, this is the kind of thing I wanted to know. I realize it could vary year-to-year but I would imagine (perhaps falsely) that it doesn't.


in this example, the B- wouldn't be 'close to median.' it would be in the bottom 30%. the B+ would be in the top 20%. The B's would be tied for class rank. so 50% of the class would report they are top 30%. but for this to actually work, they'd have to get the same grades in each class, or at least in classes with identical credit hours, every semester.

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Cade McNown
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Re: How average is "median"?

Postby Cade McNown » Thu Apr 28, 2011 6:56 pm

usuaggie wrote:the problem is your use of median. asking how many people are at median. there is only one point that is at the median. so you can't have 30 students at the median, unless they all got the exact same grades in the same credit-weighted classes.


Basically what OP is asking is, what is the probability of receiving a median grade in a given class?

Law school grades, like in most academic settings, approximate a normal bell curve distribution. Of course, grade inflation (pre-setting medians above the alphabetical middle of the distribution i.e. B+ instead of C) will positively skew the distribution. Nevertheless the number of students at the median will remain almost constant (almost because I suspect professors are reluctant to fail people). Based on a normally shaped distribution with limited grade possibilities A-F, you can roughly estimate that about 20% of a given class (read single course, not graduating class) will receive a median grade. Take whatever deductions you want from that. If the estimate is right, for instance, you can say that 60% of that class received a median grade or better.

OP, once you get through a year's courseload, the members of your graduating class will have distinguished themselves. Once everyone receives 8+ marks, the group at the median will have shrunken considerably to the point where your percentile rank will accurately represent exact placement within your graduating class (i.e. just how many people you're better/worse than).

Edit for strikethrough

Hope this helps. Short Version: Unless a school posts its distributions, the best you can do is to estimate based on normal positively skewed bell curves. Estimate about 20% at median in each course.

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California Babe
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Re: How average is "median"?

Postby California Babe » Thu Apr 28, 2011 7:01 pm

usuaggie wrote:
bdubs wrote:
TaipeiMort wrote:Some years/schools the top 10% may be the same people in every class, some schools they may be completely dispersed. For example, at uChicago the "median" grade is a 177 (B), and top-ten percent at graduation is a 179.5, which is a B+, a top 5% is something like 180.5.

I would guess the distribution is something like:

C+,B-,B-(close to median),B,B,B,B,B,B+,A

this would mean that 80% are close to median or above.


Thank you, this is the kind of thing I wanted to know. I realize it could vary year-to-year but I would imagine (perhaps falsely) that it doesn't.


in this example, the B- wouldn't be 'close to median.' it would be in the bottom 30%. the B+ would be in the top 20%. The B's would be tied for class rank. so 50% of the class would report they are top 30%. but for this to actually work, they'd have to get the same grades in each class, or at least in classes with identical credit hours, every semester.


You are confusing the difference between a median in an individual class, and a median in the class rank of averaged GPAs. Most schools that enforce a strict median grade (for instance, OP's B+), are referring to a specific class, not a GPA as a whole. Further, some schools that do this (such as mine), don't ever publish the median of the GPAs, but instead only release what the individual class median is.

EDIT: Again, the problem is trying to characterize what "median" is by taking one school's grading method and applying it to every school. As I attempted to say in my first post, every school will do this so differently that what "median" is will be different from one school to the next.

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Cade McNown
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Re: How average is "median"?

Postby Cade McNown » Thu Apr 28, 2011 7:13 pm

California Babe wrote:EDIT: Again, the problem is trying to characterize what "median" is by taking one school's grading method and applying it to every school. As I attempted to say in my first post, every school will do this so differently that what "median" is will be different from one school to the next.


Regardless of where schools set their medians, the number of students at/near the median will remain almost constant. OP was essentially asking how reliably does the median represent the exact middle of the class. If we assume normally shaped distributions, even if they are positively skewed towards higher grades (B+) or negatively skewed towards lower grades (C-), the number of students receiving median grades will not change.

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California Babe
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Re: How average is "median"?

Postby California Babe » Thu Apr 28, 2011 7:40 pm

Cade McNown wrote:
California Babe wrote:EDIT: Again, the problem is trying to characterize what "median" is by taking one school's grading method and applying it to every school. As I attempted to say in my first post, every school will do this so differently that what "median" is will be different from one school to the next.


Regardless of where schools set their medians, the number of students at/near the median will remain almost constant. OP was essentially asking how reliably does the median represent the exact middle of the class. If we assume normally shaped distributions, even if they are positively skewed towards higher grades (B+) or negatively skewed towards lower grades (C-), the number of students receiving median grades will not change.


You can't assume a normally shaped distribution unless that school requires it.

spondee
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Re: How average is "median"?

Postby spondee » Thu Apr 28, 2011 8:20 pm

OP, I think most people assume a normal distribution (at least for the above-median half of the curve) because of a lack of info otherwise.

grash
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Re: How average is "median"?

Postby grash » Thu Apr 28, 2011 11:29 pm

California Babe wrote:
Cade McNown wrote:
California Babe wrote:EDIT: Again, the problem is trying to characterize what "median" is by taking one school's grading method and applying it to every school. As I attempted to say in my first post, every school will do this so differently that what "median" is will be different from one school to the next.


Regardless of where schools set their medians, the number of students at/near the median will remain almost constant. OP was essentially asking how reliably does the median represent the exact middle of the class. If we assume normally shaped distributions, even if they are positively skewed towards higher grades (B+) or negatively skewed towards lower grades (C-), the number of students receiving median grades will not change.


You can't assume a normally shaped distribution unless that school requires it.


sure you can. in the absence of a better method (no one here's good enough to estimate a skewed fit) normality's the best you can do, so you do it and understand that your inferences might be a bit off.

that said, number of people at median differs a lot from class to class, but when you aggregate all the grades across your 1L year, there are sufficiently many gpa combinations that there should be only a handful of people at exactly median. what, in essence, starts to occur is as you accumulate grades the distribution smooths out from a discrete one to a continuous one.

*side point - NU allows 1Ls to take uncurved classes, so the idea that 3.3 is the median student is probably off. from what i understand the mean GPA is a lot higher in uncurved classes,.
Last edited by grash on Thu Apr 28, 2011 11:30 pm, edited 1 time in total.

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DallasCowboy
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Re: How average is "median"?

Postby DallasCowboy » Thu Apr 28, 2011 11:29 pm


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TaipeiMort
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Re: How average is "median"?

Postby TaipeiMort » Fri Apr 29, 2011 12:17 am

bdubs wrote:
TaipeiMort wrote:Some years/schools the top 10% may be the same people in every class, some schools they may be completely dispersed. For example, at uChicago the "median" grade is a 177 (B), and top-ten percent at graduation is a 179.5, which is a B+, a top 5% is something like 180.5.

I would guess the distribution is something like:

C+,B-,B-(close to median),B,B,B,B,B,B+,A

this would mean that 80% are close to median or above.


Thank you, this is the kind of thing I wanted to know. I realize it could vary year-to-year but I would imagine (perhaps falsely) that it doesn't.


I am just guessing, so don't take my guess as pure knowledge of Chicago's curve. However, I could see a variance among classes where you might also have:

C+,B-,B-,B-,B,B,B+,B+,A-, A

It really just depends on how many different kids get the high and low grades.

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Sogui
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Re: How average is "median"?

Postby Sogui » Sat Apr 30, 2011 9:57 pm

It smooths out like a bell curve over time, but after 1L year the distribution is still jagged due to a limited number of outcomes and the nature of our curve.

For example, a 3.24 is supposed to be class rank median while the median for any given course is 3.33. This is because a 3.24 is roughly what the curve "average" comes out as, and over time the bulk of the class will slide toward this GPA as the median.

Still, while a 3.24 is around median at the end of the year. A 3.41 is typically around top 30% and the percentiles drop off rapidly after that because few students will consistently get the A's they need to maintain anything above a 3.5. This inability for the vast majority of students to score A's/A-'s frequently is what pushes us all into a normal distribution over time. So while up to 25% of the class may score an A/A- on any given 1L exam, almost nobody will be in that same classification over and over and over... it will typically rotate people through based on how heavily they may have been interested in a class, if the study methods were conducive to that exam, if the test style favored your strengths, how much sleep you got the night before, how much time you were able to set aside to prep for that exam, professor's grading style, what the professor had to eat that morning, if your exam was after a series of particularly strong or weak exams, etc....

Overall your GPA should come to roughly conform to your ability to consistently turn in "above average" answers and beyond that it is how frequently you can piece together an "honors" exam that will earn you that coveted A-class grade. Despite this outcome, it is still really frustrating seeing how arbitrary and random the grading process can be for some professors who just don't care.




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