Medians vs. Mean

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woosah
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Medians vs. Mean

Postby woosah » Sat Nov 23, 2013 12:40 pm

I'm sorry if this question has been asked before and it's pinned somewhere. I couldn't find it.

I am curious as to why law schools consider the "Median LSAT and GPA" and not the "Mean LSAT and GPA." Can anyone explain to me what their reasoning is?

Also, while I understand it's mathematically possible for the median of a set of numbers to be much different from the mean, I have a hard time understanding HOW that happens.

For example, Northwestern has a 25th of 163 and a 75th of 170, yet their median is 169. Again, I realize this is probably a simple mathematical question... But I'm really having trouble understanding how that happens. If someone could help me out, I'd appreciate it.

NanaP
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Re: Medians vs. Mean

Postby NanaP » Sat Nov 23, 2013 12:43 pm

woosah wrote:I'm sorry if this question has been asked before and it's pinned somewhere. I couldn't find it.

I am curious as to why law schools consider the "Median LSAT and GPA" and not the "Mean LSAT and GPA." Can anyone explain to me what their reasoning is?

Also, while I understand it's mathematically possible for the median of a set of numbers to be much different from the mean, I have a hard time understanding HOW that happens.

For example, Northwestern has a 25th of 163 and a 75th of 170, yet their median is 169. Again, I realize this is probably a simple mathematical question... But I'm really having trouble understanding how that happens. If someone could help me out, I'd appreciate it.



It's to their advantage to use the median....higher than the mean

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ManoftheHour
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Re: Medians vs. Mean

Postby ManoftheHour » Sat Nov 23, 2013 1:09 pm

woosah wrote:I'm sorry if this question has been asked before and it's pinned somewhere. I couldn't find it.

I am curious as to why law schools consider the "Median LSAT and GPA" and not the "Mean LSAT and GPA." Can anyone explain to me what their reasoning is?

Also, while I understand it's mathematically possible for the median of a set of numbers to be much different from the mean, I have a hard time understanding HOW that happens.

For example, Northwestern has a 25th of 163 and a 75th of 170, yet their median is 169. Again, I realize this is probably a simple mathematical question... But I'm really having trouble understanding how that happens. If someone could help me out, I'd appreciate it.


Let's say X law school had the following students with these LSAT scores:

121, 122, 122, 123, 125, 162, 163, 163, 163, 163, 164

The median would be 162. Mean would be much lower. Can you see how in this set of numbers the 25th and 75th percentile would be pretty far apart? This is how schools game their numbers.

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Tiago Splitter
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Re: Medians vs. Mean

Postby Tiago Splitter » Sat Nov 23, 2013 1:14 pm

woosah wrote:I'm sorry if this question has been asked before and it's pinned somewhere. I couldn't find it.

I am curious as to why law schools consider the "Median LSAT and GPA" and not the "Mean LSAT and GPA." Can anyone explain to me what their reasoning is?

Also, while I understand it's mathematically possible for the median of a set of numbers to be much different from the mean, I have a hard time understanding HOW that happens.

For example, Northwestern has a 25th of 163 and a 75th of 170, yet their median is 169. Again, I realize this is probably a simple mathematical question... But I'm really having trouble understanding how that happens. If someone could help me out, I'd appreciate it.

US News uses the median, which is why schools care about it.

Northwestern gets numbers like that by using splitters (high LSAT/low GPA) and reverse-splitters (high GPA/low LSAT) to maximize their medians.

What essentially happens is that schools look for 50% of their incoming class to be at or above the target median. Once they get that number, they stop being concerned with that number, so the scores tend to drop rapidly below the median. This is why it's so important to have at least one number at or above a school's median; at a place like Northwestern with medians of 3.7/169 you are much better off with a 2.8/170 than you are with a 3.6/168.

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CitrusFruit
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Re: Medians vs. Mean

Postby CitrusFruit » Sat Nov 23, 2013 2:25 pm

1. How much do schools value their 75th percentiles?
2. Is being exactly at the median or 75th good enough to help them, or do you need to be above it? I have run into this issue with my GPA being exactly at some schools' 75th.

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2014
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Re: Medians vs. Mean

Postby 2014 » Sat Nov 23, 2013 3:04 pm

Their 75th's should have little importance. They put them on their marketing, but the main concern is US News which only cares about median. For schools with tight ranges, (i.e. Median at 169, 75th at 170) being at the 75th might be marginally more useful because you represent a chance for them to increase their median, but for that school I don't see why a 171 would be any different than a 170.

I will say there might be a caveat for big splitters since schools do at least claim to have some sort of concern for whether they are admitting students who can handle the course load since they want people to come in, succeed, and be employable. If you have a below 25th LSAT/GPA it probably helps to have the other one above the 75th to paint a better picture for your potential. It still is dwarfed heavily by the importance of being at the median though.

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CitrusFruit
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Re: Medians vs. Mean

Postby CitrusFruit » Sat Nov 23, 2013 3:26 pm

2014 wrote:Their 75th's should have little importance. They put them on their marketing, but the main concern is US News which only cares about median. For schools with tight ranges, (i.e. Median at 169, 75th at 170) being at the 75th might be marginally more useful because you represent a chance for them to increase their median, but for that school I don't see why a 171 would be any different than a 170.

I will say there might be a caveat for big splitters since schools do at least claim to have some sort of concern for whether they are admitting students who can handle the course load since they want people to come in, succeed, and be employable. If you have a below 25th LSAT/GPA it probably helps to have the other one above the 75th to paint a better picture for your potential. It still is dwarfed heavily by the importance of being at the median though.


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Last edited by CitrusFruit on Sat Nov 23, 2013 4:04 pm, edited 1 time in total.

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2014
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Re: Medians vs. Mean

Postby 2014 » Sat Nov 23, 2013 3:44 pm

CitrusFruit wrote:
2014 wrote:Their 75th's should have little importance. They put them on their marketing, but the main concern is US News which only cares about median. For schools with tight ranges, (i.e. Median at 169, 75th at 170) being at the 75th might be marginally more useful because you represent a chance for them to increase their median, but for that school I don't see why a 171 would be any different than a 170.

I will say there might be a caveat for big splitters since schools do at least claim to have some sort of concern for whether they are admitting students who can handle the course load since they want people to come in, succeed, and be employable. If you have a below 25th LSAT/GPA it probably helps to have the other one above the 75th to paint a better picture for your potential. It still is dwarfed heavily by the importance of being at the median though.


If that's true then a 4.1 180 should be only marginally more appealing to schools than a 3.85 173. What a dumb system that would be...

Make it 4.1 180 compared to a 3.9 173 and both get full rides at CCN on down. Do you think the admissions folks at Columbia should pat themselves harder on the back when the former matriculates or something? They both get in and get the same scholarship offer, any difference since very marginal.

When you throw Y and S into the mix, they have small enough classes that they are choosing between a pool of people who all have stellar numbers so maybe they care more about those differences as a means of differentiation.

woosah
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Re: Medians vs. Mean

Postby woosah » Sat Nov 23, 2013 7:11 pm

at a place like Northwestern with medians of 3.7/169 you are much better off with a 2.8/170 than you are with a 3.6/168.


This example is exactly why I am confused with this system!

So the law schools are interested in the median because US News reports the median... But now the question becomes, why would US News report the median? It creates a situation, as Tiago Splitter points out, where a candidate that sits at 2.8/170 is more valuable than one that sits at 3.7/169.

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midwest17
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Re: Medians vs. Mean

Postby midwest17 » Sat Nov 23, 2013 7:18 pm

woosah wrote:
at a place like Northwestern with medians of 3.7/169 you are much better off with a 2.8/170 than you are with a 3.6/168.


This example is exactly why I am confused with this system!

So the law schools are interested in the median because US News reports the median... But now the question becomes, why would US News report the median? It creates a situation, as Tiago Splitter points out, where a candidate that sits at 2.8/170 is more valuable than one that sits at 3.7/169.


Medians are generally more meaningful. An outlier doesn't affect the overall quality of a student body nearly as much as averaging suggests. Taking medians also gives schools more flexibility to not be entirely numbers driven, if they don't want to be.

I don't think they should *only* look at medians, since that does create some weird discontinuities. But averaging probably isn't the way to go either. The right solution is probably to look at the quartiles as well.

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cotiger
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Re: Medians vs. Mean

Postby cotiger » Sat Nov 23, 2013 8:24 pm

woosah wrote:
at a place like Northwestern with medians of 3.7/169 you are much better off with a 2.8/170 than you are with a 3.6/168.


This example is exactly why I am confused with this system!

So the law schools are interested in the median because US News reports the median... But now the question becomes, why would US News report the median? It creates a situation, as Tiago Splitter points out, where a candidate that sits at 2.8/170 is more valuable than one that sits at 3.7/169.


Using means would make them even more numbers driven. Think about it this way:

School A: 169, 169, 169, 169, 169
School B: 160, 171, 171, 171, 171

A/B means: 169/168.8 (School A higher)
A/B medians: 169/171 (School B higher)

Which student body do you think is better?

Using medians allows schools to be more holistic on the lower end of the scale. They can let in that 160 person who is clearly amazing but just sucks at the LSAT because they won't really affect their scores. Using means, though, means that that 160 is going to have a huge effect. Right now, below median is below median, so schools can pick and choose which candidate they really think is best. Using a mean, the exact value of those below median scores count, so schools would be incentivized to be even more ruthlessly numbers driven.

woosah
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Re: Medians vs. Mean

Postby woosah » Sat Nov 23, 2013 9:30 pm

cotiger wrote:
woosah wrote:
at a place like Northwestern with medians of 3.7/169 you are much better off with a 2.8/170 than you are with a 3.6/168.


This example is exactly why I am confused with this system!

So the law schools are interested in the median because US News reports the median... But now the question becomes, why would US News report the median? It creates a situation, as Tiago Splitter points out, where a candidate that sits at 2.8/170 is more valuable than one that sits at 3.7/169.


Using means would make them even more numbers driven. Think about it this way:

School A: 169, 169, 169, 169, 169
School B: 160, 171, 171, 171, 171

A/B means: 169/168.8 (School A higher)
A/B medians: 169/171 (School B higher)

Which student body do you think is better?

Using medians allows schools to be more holistic on the lower end of the scale. They can let in that 160 person who is clearly amazing but just sucks at the LSAT because they won't really affect their scores. Using means, though, means that that 160 is going to have a huge effect. Right now, below median is below median, so schools can pick and choose which candidate they really think is best. Using a mean, the exact value of those below median scores count, so schools would be incentivized to be even more ruthlessly numbers driven.


Good point. That a 2.9/170 is more valuable than a 3.6/168 is still problematic, in my opinion... But I understand at least a partial reason for their system now. Thanks.

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banjo
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Re: Medians vs. Mean

Postby banjo » Sat Nov 23, 2013 9:46 pm

cotiger wrote:Using medians allows schools to be more holistic on the lower end of the scale.


Yes, I think this is the reason. USNWR doesn't want to punish schools for admitting lower LSAT scores in order to achieve a well-rounded, diverse student body.

SPerez
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Re: Medians vs. Mean

Postby SPerez » Mon Nov 25, 2013 12:49 pm

My understanding is that USNWR uses medians because that's what law schools were already using, but I could be wrong about that. Although I, unlike the majority of people on TLS, was actually alive in 1987 when the first USNWR rankings came out (only listing the top 20, BTW), I can't say this is something I've been following since then. :P

As others have said, medians allow a school to admit in a more holistic way (like I assume you all want us to do). Like other things, this plays out slightly different at the elite schools than it does for the rest of us.

I remember being at a conference and someone asked a question (I forget what it was now). The panelist was an admissions dean from an elite school, and their answer included something like "...and we can take a chance on someone with a 163..." I remember rolling my eyes pretty hard at the notion someone with a 160+ and good gpa was somehow "risky", especially with the grade inflation at the top schools. That person would probably be law review/near the top of the class at all but a handful of law schools and go on to be an excellent lawyer.

For the schools I've worked at, the "chances" we take are often people who have no other options or their other options are bad ones. They might have old GPAs that don't tell the whole story. Or they might have LSATs in the high 140s, yet also have a history of outperforming standardized tests, etc. Using medians allows us to have a more interesting class by allowing us to take those diamonds in the rough.

Dean Perez

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ScottRiqui
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Re: Medians vs. Mean

Postby ScottRiqui » Mon Nov 25, 2013 1:05 pm

Moved to different thread.




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