<p>By that logic, if school X has a wider range like, say, 600 780, it would have even higher percentage like, say, 25% of 800? That makes no sense; what you did is double-counting. You mentioned COE at Cornell. Well, it’s the COE that “stretches” Cornell’s upper range to Duke’s level. Without COE, it would be lower. COE has already been accounted for. You don’t go back to arbitrarily bump up the percentage of 800 even higher for Cornell.</p>
<p>I know all those were just your guesstimates; I just want to point out your methodology has an obvious flaw.</p>
<p>FYI: Cornell’s engineering school is not “packed with 780-800s math”. I’d seen the range before (they used to put it on the web) and it’s actually very similar to the overall range of schools like Dartmouth.</p>
I’ll use an example to make it simple. Consider 2 distributions. </p>
<p>Distribution 1: Duke 25th and 75th Percentile Scores
Distribution 1 is an ideal normal distribution. It has an 25th and 75th percentile score of 690 and 780, like Duke. This group has an expected 16% chance of 800 SAT, like the listed approximation for Duke.</p>
<p>Distribution 2: Cornell 25th and 75th Percentile Scores
Distribution 2 contains all of the points of distribution 1 along with a second group, with expected lower scores. Everyone in the low scoring group received well under the 690 25th percentile SAT. I’ll call this group the hotel school. 11% of the freshman class is required to be in the hotel school group to bring the 25th percentile score down to 670, like Cornell. However this 11% at the bottom also brings down the 75th percentile score from for the overall class from 780 to 760. In order to maintain a score of 780, like Cornell, then the non-hotel group needs to get stronger, with a 75th percentile SAT for this non-hotel group increasing from 780 to slightly above 790. 89% in non-hotel group * 22% predicted 800 chance for the 790+ Math (using normal approximation) = 19-20% chance of 800 SAT in overall class. The expected chance of 800 SAT increased for the overall class, even though the 25th percentile decreased.</p>
You are totally double counting again and you assume everyone at the hotel school is dumber than everyone else at Cornell. If you compare Cornell’s COE with Stanford’s overall ranges, you’d see Cornell’s 75th percentile probably barely reaches 800. That’s not “packed with 780-800” in my book. That’s minor anyway. What’s more important is for you to realize there is nothing special about 720-800 on Math for COE and that Cornell isn’t the only one that has an enginereing school. I am sure Duke’s engineering school has similar range and maybe even higher. So are other top private’s COE. </p>
<p>In fact, if you use the on about.com and assume the midpoint as the average, it’s 1465 for M+CR. In reality, the average is usually slightly less than the midpoint actually but I’d let this slide. Well, Northwestern’s average is 1480. You can see Cornell’s non-hotel group isn’t really as great as you asserted.</p>
<p>I did not think that is was necessary to explain that an example in which 100% of a group gets extremely low scores was an example to show a lower 25th percentile coinciding with an increased chance of 800, rather than a result using actual data. I suppose even that is not obvious to some.</p>
<p>I’ll spell it out in more detail this time. You have the Duke distribution and add a 2nd distribution to the Duke distribution. Everyone in the 2nd distribution gets a low math score. This brings down the 25th SAT for the overall class down to Cornell level, but it also brings the 75th percentile to below Cornell level. To match the 75th percentile of the Cornell group, the upper end of the scores need to increase. This means Duke distribution group needs to have higher scores. The higher scoring group needs to have a 75th percentile above the Duke 75th percentile of 780. Assuming a normal distribution, it works out to a 75th percentile of slightly above 790 for this high scoring group, resulting in a ~22% chance of 800 for this high scoring group. </p>
<p>The overall 75th percentile is entirely determined by this group that has scores above the Duke distribution. If 89% of the class is in the group that has scores above Duke, then the chance of an 800 for the overall class is calculated by 89% of class in high scoring group * 22% chance of 800 for high scoring group = 19-20%. </p>
<p>There is no double counting. The high scoring group is counted once by the 89% * 22% factor and the low scoring group is counted once by the 11% * 0%. Note that the overall result is 19-20%, not the Cornell value in listed in the table because this is example to show a lower 25th percentile coinciding with an increased chance of 800, rather than a result using real data.</p>
<p>
The whole focus of this discussion was the chance of an 800 score is primarily determined by the upper end of the distribution, not the average score. If a college has a 25th percentile of 740 and 75th percentile of 750 for a 1490 M+CR, does that mean they have an increased chance of 800 over the schools we have been discussing with much higher 75th percentile scores , or an increased chance of 800s than suggested by the 75th percentile 800 listed for Cornell engineering?</p>
It was an example to show how a lower 25th percentile can coincide with a higher chance of 800. It was not using real data. That said, I do think it’s safe to assume that the hotel school has a smaller rate of 800 math scores than the overall student body and much smaller rate the engineering school. Posts on CC from several years ago mentioned SAT averages of 1300 and 1320 math + CR for the hotel school. I don’t know if this is accurate or what the score is today.</p>
<p>
You seem to have trouble understanding that examples can be made to show a point without using real data. When I wrote, ". If a college has a 25th percentile of 740 and 75th percentile of 750 for a 1490 M+CR, does that mean they have an increased chance of 800…" I was obviously not talking about Northwestern’s scores. It was an example to show that average score does not dictate chance of 800, and as a score range becomes more narrow in can indicate a reduced chance of 800. Also note that Cornell engineering school’s math average is far above Northewestern’s overall class average. It’s actually above the math average for all the overall class of all colleges except Caltech, MIT, and Mudd. There is no point to comparing verbal scores when discussing rate of 800s on math.</p>
<p>^^Edit: sorry I had to delete my post cos I was about to get interrupted but didn’t finish my post.</p>
<p>You assumed Cornell somehow got two very different distributions and somehow the non-hotel group at Cornell is stronger than Duke’s student body in math. That’s essentially what you are implying. Let’s step back and look at the big picture. Why would Cornell, after excluding the hotel students, have higher fraction of student body with 800 on math than Duke does. Does it even make sense? You can substitute Duke with Penn if that makes it easier. Once you do that, you should easily see there’s something wrong with your assumptions.</p>
<p>You really don’t need to make it so convoluted because CDS already provides the ACTUAL percentage of students in the 700-800 range. According to you, because of the hotel group, Cornell must have higher fraction in the 700-800 range than their peers to bring its overall range close to its peers. Well, let’s look at what CDS say:</p>
<p>Cornell
700-800M 66%
700-800CR 47%</p>
<p>Northwestern
700-800M 68%
700-800CR 60%</p>
<p>Penn
700-800M 71%
700-800CR 60%</p>
<p>Note that Penn and Northwestern have higher percentage, not lower, with 700-800 range in math, though the difference isn’t significant. The difference is more significant in verbal. But you seemed to underestimate that difference in post #34 because you overrated the impact from the hotel group. I DO understand where you come from but the impact isn’t really as big as you think. Cornell isn’t special either to have a college with weaker scores. Northwestern got music and communications schools. Penn got nursing school. These are just examples. What these all mean is that the hotel group doesn’t impact as much as you may expect and that Cornell’s distribution isn’t really as wacky as you may think and isn’t so different from many others’ after all. You really don’t need to have a special treatment for only couple, in this case, Cornell and Berkeley (don’t get this one at all) but not others.</p>
As I have repeatedly stated, the 2 distributions example was an example to show that a lower 25th percentile SAT score can coincide with an increased rate of 800. It was not the score of the actual hotel school. Unfortunately I do not have real numbers for the different Cornell schools, such as the hotel school. As I’ve explained repeatedly, an increased number of scores on the lower end pull down the 75th percentile. So in order to maintain a constant 75th percentile, the number of scores on the upper end need to increase as the number of scores on the lower end increase. </p>
<p>When you make a normal distribution assumption (not 2 distributions, everything in one normal bell curve), then the range of high end outliers increases as the standard deviation of the curve increases. I thought this concept would awkward to associate to colleges, particularly with hitting a max score rail, so I used an example with 2 distributions to make a more obvious point and provide a plausible explanation. I don’t know how else to explain, aside from repeating earlier posts, but I’ll try to answer your question in a different way.</p>
<p>You asked why would Cornell, after excluding the hotel students, would have a higher fraction of student body with 800 on math than Duke does. Lets say that the school at Cornell that has the lowest math SAT scores composes 20% of freshman class. The low scoring school has mid 50% range of 650/730, and the rest of the class has mid 50% range of 700/790. This results in a 75th percentile of 780, when assuming both groups have a normal distribution. Note that I do not have real numbers, so I cannot use real numbers. These numbers are only examples to make a point. I repeat that they are not real numbers for the school. There is no way to make a 75th percentile of 780 for the full class without having the higher scoring group have a 75th percentile above 780.</p>
<p>
The many examples I’ve listed all had cases with fewer 700s because of increased scores on the low end, yet they all showed an increased rate of scores at the high end . As the rate of low end scores increased, the rate of high end scores needed to also increase to maintain a constant 75th percentile score. That was the whole point of my posts.</p>
<p>Okay, now that I read your posts more carefully, I understand where you come from. That said, it still feels a bit strange that a school with lower percentage of 700-800 would have a higher percentage of 800. I wonder if your assumed ranges for some of the high scoring groups may be too high. For example, the 75th percentile of non-hotel group may stay at 780 or only slightly above it, not slightly above 790 as you assumed, given that the hotel group is a tiny fraction of the school. Also, Cornell isn’t the only school with a low scoring school; Northwestern does too and a bunch of Big Ten athletes while Penn has a nursing school. Perhaps the kind of upward adjustments you made is probably not necessary.</p>