Statistical Question- Law School LSAT Range Forum

[3ThrowAway99]

How is 25th-75th percentile band statistically derived? I understand that it represents the fact that the bulk (50%) of all students at that particular school fall within this range in terms of LSAT score (with a lower quartile of the students falling below this range and an upper quartile falling above this range), but how is it that some of the ranges are much wider than others? I guess you just literally take the middle 50% of the total number of scores and whatever the end points are (the extremes- lowest and highest individual numbers of this grouping) determines the range? Is it that simple?

Also, I have seen info that seems to indicate that the median LSAT score for a given school tends to be at the very upper end of this 25-75% percentile range. This has been confusing to me because I had the impression that this 25-75% percentile range represents a relatively evenly distributed score band (meaning that seeing a range of let's say 160-168 I would think that a 164 or 165 would be a pretty competitive score for that school because I assumed the approximate mean and/or median of the band fell around 164). However, if the band is calculated as described above and if the schools median LSAT is typically at the very upper end of the 25-75th band, then I think this could mean I have looked at this all wrong.

I am now thinking that comparing my score (or any given individual's score) to the school's median rather than where it falls in relation to the 25'th-75th range is likely to be much more predictive of acceptance at a given school. This is based on the idea that the 25-75th range does not represent a relatively even distribution of scores but rather just shows where the low and high points of the middle 50% of scores fall, with most of them probably actually falling toward the high part of the range given that overall median tends to be right around the high point.

Could someone who understands the basic statistical principles related to this weigh in?

[Knock]

I think it's like, 25th = 25% of people had that LSAT or lower, 50th = 50% had that LSAT or lower, 75th = 75% had that LSAT or lower.

So like for Columbia, which has 25th at 170, median (50th) at 172, and 75th at 175, that just means 25% have a 170 or lower, 50% have a 172 or lower, 75% have 175 or lower.

Median is definitely going to be more useful when determining your likelihood of acceptance.

[Eugenie Danglars]

To find a median layman's style: Line up all the numbers small to large, then pick up the one in the middle. That's your median.

Example:
12 15 19 20 23 25 32

Median here is 20.

The interesting example (for law school admissions at least) is this:

0 0 1 20 500 750 12034857829

Median is still 20.

25th and 75th percentiles are calculated similarly.

In theory, once you're above the 75th or below the 25th, your score shouldn't matter much. So if a school's 25th is 165, they shouldn't statistically prefer a 164 to a 150. Of course, in real life, it doesn't work this way, but it's cool, right?

[kazu]

To find a median layman's style: Line up all the numbers small to large, then pick up the one in the middle. That's your median.

Example:
12 15 19 20 23 25 32

Median here is 20.

The interesting example (for law school admissions at least) is this:

0 0 1 20 500 750 12034857829

Median is still 20.

25th and 75th percentiles are calculated similarly.

In theory, once you're above the 75th or below the 25th, your score shouldn't matter much. So if a school's 25th is 165, they shouldn't statistically prefer a 164 to a 150. Of course, in real life, it doesn't work this way, but it's cool, right?

To add to this, the reason law school LSATs medians are closer to the 75% is because their admittances become something like this:

0 5 10 15 20 70 71 72 73 74 75

Obviously this is a bit exaggerated, but above the median would be 70, the 25% would be 10 (the score of the person at the 25% line from the bottom), and the 75% would be 73.

[3ThrowAway99]

I think it's like, 25th = 25% of people had that LSAT or lower, 50th = 50% had that LSAT or lower, 75th = 75% had that LSAT or lower.

So like for Columbia, which has 25th at 170, median (50th) at 172, and 75th at 175, that just means 25% have a 170 or lower, 50% have a 172 or lower, 75% have 175 or lower.

Median is definitely going to be more useful when determining your likelihood of acceptance.

I think I understand the basics you mentioned in the first part of your post fairly clearly (I hope my post didn't give the impression that I do not). In any case, regarding your understanding that 50th percentile represents median, I am trying to understand (in part) how this assessment is not displaced given that the median score for each school actually falls very close to the 75th%percentile of LSAT score for that school. I realized that at the very least 25th/50th/75th percentile marks don't fall anywhere close to a 'flat' (this might not be the correct term to designate what I mean) distribution (e.g. U of MN has a 75th%tile of 168, but I believe their median is 167; SMU has a 75th of 165 with a median of 164).

Insofar as median does relate directly to 50th percentile (which I would like to confirm further, though it seems to make perfect sense), it just shows that 50th%tile is extremely skewed toward the 75th%tile in terms of actual number scores such that they are almost the same number. I suppose this could be possible given that a school will likely tend to take applicants who cluster fairly tightly around their median, and those above the median will probably for the most part be only slightly above it, thus restricting the quartile immediately above the 50th percentile to a very narrow range (the ones considerably above it are likely to go to a better school for one thing in many cases).

Also, the 50-75%tile could even include a portion of the LSAT scores consistent with the median number, since the same number score could represent both the median cut-off and a portion of the quartile immediately above the median (50th-75th) where the percentile cutoffs are based on actual ordered scores in a series rather than on a pre-set distribution.

The clustering around median, in some cases with a portion of the same individual median LSAT scores being counted for the quartile immediately below median and some for the quartile immediately above, and in all cases with those LSAT numerical scores immediately above the median number being counted toward the 50th-75th, could help to fill the 50'th-75th "quickly," and help explain why the 50th%tile is so close in terms of numerical LSAT score to the 75th. Conversely, the 50th percentile of an actual ordered number scale would not necessarily include all scores that are consistent with the top number of the 50th percentile (some of the identical number scores to the median could actually be included in the scores counted toward the 50-75th percentile instead), and the 50th percentile would also include numbers progressively less strongly clustered as they progress away from the median which would disproportionately expand the range of the 0-50th percentile more than the 50-75th.

[3ThrowAway99]

To find a median layman's style: Line up all the numbers small to large, then pick up the one in the middle. That's your median.

Example:
12 15 19 20 23 25 32

Median here is 20.

The interesting example (for law school admissions at least) is this:

0 0 1 20 500 750 12034857829

Median is still 20.

25th and 75th percentiles are calculated similarly.

In theory, once you're above the 75th or below the 25th, your score shouldn't matter much. So if a school's 25th is 165, they shouldn't statistically prefer a 164 to a 150. Of course, in real life, it doesn't work this way, but it's cool, right?

To add to this, the reason law school LSATs medians are closer to the 75% is because their admittances become something like this:

0 5 10 15 20 70 71 72 73 74 75

Obviously this is a bit exaggerated, but above the median would be 70, the 25% would be 10 (the score of the person at the 25% line from the bottom), and the 75% would be 73.

Thanks- that seems to be a nice illustration of the typical clustering effect.

[WestOfTheRest]

If it makes you feel better, Harvard and Yale both appear to have a normal distribution based on their percentiles.

[rundoxierun]

OP, think of 25th/median/75th numbers as "at least" numbers. For instance, a 25th percentile of 164 means AT LEAST 25% of the class scored at or below 164. It could be that 30% scored 164 or below, it could be that 30% scored exactly 164 and no one actually scored below.

[09042014]

This isn't really a hard concept wtf is wrong with you.

[capitalacq]

This isn't really a hard concept wtf is wrong with you.

liberal artsy majors

[CanadianWolf]

I understand your question & have had similiar thoughts on this matter as you. I don't know the answer in mathmatical terms, but will continue with the simplistic, and often correct, understanding expressed by the other posters here as well as by USNews.
The best way to evaluate your LSAT score is to utilize both the 25th & 75th percentile ranges as well as that law school's median LSAT score for matriculated students.
The concepts are quite simple, but it can be distressing when one sees a law school's mid-range at 166 to 172, but the median is 171.
P.S. I have read a few internet discussions in which a college or university's undergraduate figures show the matriculated first year students' median SAT as being above the 75th percentile figure for that school. Speculation runs from different year's data used to certain matriculated categories (e.g. URMs & development cases) were omitted from one set of data.

[Bumi]

The concepts are quite simple, but it can be distressing when one sees a law school's mid-range at 166 to 172, but the median is 171.8.

A median of 171.8? This thread is classic.

[270910]

This isn't really a hard concept wtf is wrong with you.

[CanadianWolf]

Corrected to 171. Thanks. I was trying to emphasize the OP's point of a cause of frustration for some.
OP: When you saw the numbers for a particular law school were they contained in the same article or from different sources even though addressing the same year ?

[bycron77]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

[Pozzo]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

WUT.

[UVA2B]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

This was a pretty useless 7 year old necro. I mean this with all due respect, but why?

[snowball2]

The interesting example (for law school admissions at least) is this:

0 0 1 20 500 750 12034857829

Median is still 20.

That's generally teh rationale for using median over mean, it eliminates any impact from outliers. So if you still had 0 at the bottom and your ridiculously large number at the other end and every number in between was one, you'd have a distorted and inflated view if you used mean instead.

[Veil of Ignorance]

.

[bycron77]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

WUT.

What does WUT mean?

[Future Ex-Engineer]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

WUT.

What does WUT mean?

He's asking Whythehell U Triedsohard

[Greenteachurro]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

WUT.

What does WUT mean?

like whyd you revive this thread? from like 7 years ago... about like basic math

[ggmu1992]

7 YEAR UPDATE:

Last year, Lawquacious worked 3400 hours instead of 2400, because no one told him he was supposed to carry the 1's when adding

[bycron77]

In the unlikely event that anyone still reads this, here are my two cents.

I have noticed and been curious about the same phenomenon -- that many LSAT medians seem to be near the upper bound of the interquartile range. I think the forest has been lost for the trees in this discussion. The OP obviously understands the basic statistics involved, and I don't know if that was the point of the post. Maybe it was and I'm just projecting my own curiosity.

To me, the real question is not how this phenomenon is statistically possible (that is pretty straightforward). The real question is, from a practical perspective, why is this happening and what does it reflect about law schools' intentional admissions practices? As has been illustrated by the statistical explanations here, medians don't always paint a very accurate picture of the kind of score you could expect to see if you picked a Law School X student's name out of a hat. As individual applicants, ideally we'd like to be able to say that if we picked a student's name out of a hat the odds would be pretty good that his LSAT score is between, say, 164 and 166. That would help us break down the pool into individuals to whom we could compare ourselves. Medians don't necessarily provide this information, which for different reasons is also true of means (e.g., per capita income in the U.S.).

The theory that people who are above the 75th percentile are above it by only a little bit would make sense for schools with such high 75th percentile LSAT scores that there is little room to go up from there, but I don't know why it would apply to schools whose scores are closer to the middle. Presumably, a school whose 75th percentile score is, say, 165 would love to drive up that number by getting as many scores over 175 as it could get. Schools are not looking to prevent upward mobility in their LSAT scores. I would think schools are likely to get enough applicants that the range of applicant scores would be large. It might be the case that a school gets a decent number of uncharacteristically high scores from applicants who see it as their safety school. And some people will end up going to their safety school.

This leads me to wonder if law schools have somewhat bimodal LSAT distributions such that they accept some number of applicants at the lower end of the score range because they have non-quantitative factors that are desirable enough to schools that schools are willing to bend on the numbers. In that scenario, for applicants who don't have exceptionally desirable non-quantitative factors, schools would care mostly about the numbers, which would drive up upper range scores. This is pure speculation. I'd be interested if anyone else knows of or has hypothesized this or some other qualitative explanation for this statistical phenomenon.

WUT.

What does WUT mean?

He's asking Whythehell U Triedsohard

That's a fair question. The answer? Bored at work, obsessively awaiting June LSAT results. But how the hell is anybody supposed to intuit that acronym?

[Pozzo]

That's a fair question. The answer? Bored at work, obsessively awaiting June LSAT results. But how the hell is anybody supposed to intuit that acronym?

Fair answer. I blame my own boredom for my asinine repsone. I just though it was a curious thing to necro this sort of thread. And Future Ex was making up an acronym for me. (props, btw) It's just an internet/troll spelling of "what?"