<p>Can we take the median number of the 25th-75th percentile range and assume it is the 50th percentile of the entire statistic?</p>
<p>For example, if a school posts 650-750 as their CR range, could we say that half scored over 700 while the other half scored below?</p>
<p>Sorry, I should have written median instead of mean in #19.</p>
<p>flyingllama, If we know the 50th score in that range, yes it is the 50th of whole.
Can assume it is approximately the mean of 25th and 75th? It depends on score distribution in that range. In selective schools, I suppose that the density would be somewhat reduced toward lower scores so that total average and median score would be well above the mean of 25th score and 75th score.</p>
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<p>I’m curious, are there state schools that are not public?</p>
<p>@flyingllama</p>
<p>No you can’t. SAT scores are normally distributed. You can’t just take the mean of 25th and 75th score for the median score.</p>
<p>noobcake, “not” normally distributed. right?</p>
<p>It IS normally distributed.</p>
<p>noobcake, even for all test takers, we do not know whether the scores are normally distributed (in exact sense). For enrolled students in a particular college, distribution would hardly be normal.</p>
<p>To add, necessary and sufficient condition that median=mean is symmetry of the distribution. (normal is sufficient.)</p>
<p>I am sorry, symmetry may be also only a sufficient condition. Let me look to it.
Anyway, it’s hard to estimate what is the mean and the median score only with 25th and 75th scores.
My gues is that 0.75<em>75th+0.25</em>25th would make some conservative sense of the mean and median score for selective schools.</p>
<p>All SAT scores are roughly normally distributed roughly at least.</p>
<p>For any set of SAT scores at a certain college, the scores are part of a normal distribution (but of course not normal by themselves.) Thus when given the 25th and 75th percentile scores and the standard SAT normal distribution, we can make an educated guess about the 50th percentile at a school.</p>
<p>question: Are there state schools that are not public?</p>
<p>chaos akita: technically yes because they give instate tuition</p>
<p>Cornell(for one or a couple of the schools)</p>
<p>TCNJ</p>
<p>off the top of my head…theres more tho</p>
<p>i think theres a couple in virginia </p>
<p>William and mary? not sure…any1 from virginia know?</p>
<p>Yeah, sure:</p>
<p>Cornell and Alfred University are the only ones.</p>
<p>[The</a> College of New Jersey - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/The_College_of_New_Jersey]The”>The College of New Jersey - Wikipedia) - PUBLIC</p>
<p>[The</a> College of William & Mary - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/The_College_of_William_and_Mary]The”>College of William & Mary - Wikipedia) - PUBLIC</p>
<p>If you don’t trust wiki, I can give you way more sources.</p>
<p>lol wasnt sure bout the virginia one. wow tcnj is public? its treated like a private</p>
<p>SAT scores are generally distributed pretty normally, even at the individual school level. If a school has 25th-75th percentile SAT M score of 650-750, you can reasonably assume that the median is right at 700. Now, it might be 690 or 710, but barely (and does not really make much difference?). As far as average scores go, I have found, through schools that publish both the ranges and the mean, that in schools that have high SAT scores, the averages are actually slightly lower than the median, while in schools that have low SAT scores, the averages are slightly higher than the median. This makes sense because the upper bound of SAT score is 1600 (CR + M). At a school with high scores, there are some (athletes, for example) with very bad scores who will bring down the average somewhat while not affecting the median or the IQR (interquartile range).</p>
<p>“SAT scores are generally distributed pretty normally, even at the individual school level.”</p>
<p>This is true for the overall general population, but how do you know how well it applies to individual schools? Have you seen data? </p>
<p>My own guess is that for many selective colleges the distribution deviates from a normal distribution. Both tails are likely to be truncated. They won’t admit so many students with low stats, and many students with much higher stats will tend to go to more selective colleges. The distribution might well be skewed, or even multimodal.</p>
<p>The scores may be normally distributed in the underlying general population , but the selection criteria of both the colleges and the students is not random, and that probably causes the distribution at a particular college to deviate from a normal distribution, is my thinking.</p>
<p>SAT scores are design to make a normal distribution roughly by its function of converting raw scores to SAT scores. But if raw scores have multiple peaks of distribution, no good converting function can be found to make a normal distribution.
As for individual schools, we cannot say many things with 25th and 75th scores. Look at MIT’s 75% SAT Math score. It’s 800. So more than 25% students have 800. How can we say those Math scores are normally distributed?</p>
<p>“Adding up the 3 50th percentile scores gives you the average composite score for the college”-- what’s wrong with this?</p>
<p>^ The 25th-75th percentiles give you what percentage of the class has a score at or above a certain level for an individual section. What score a person got on writing has no statistical bearing on what he/she got on math, so you can’t just extrapolate other section scores based on one section.</p>