<p>Admission statistics are self-reported by the schools, i.e. they are not audited data, so take what you may from it. I have looked at the data available online and find that the data can be presented in a way that makes the school look better and can easily be manipulated. Case in point, take for example, the data available for Andover. Last year they had 3160 applications, 14% admit rate, so the number of admits is 442. This year they had less number of applicants 3029 and only admitted 402 (40 less students than last year) and as a result they claim their admit rate dropped to 13%. This is artificial. For example, Andover has more than 100 day students which they can use to admit a lower number of day students, still fill all their boarding beds, and make it look like their overall admit rate has dropped. If they had admitted the same number of students as last year 442, their admit rate would have increased to 15%. Obviously the pressure to report better stats seems to have taken over.</p>
<p>Another number to look at is the 94% average SSAT score they reported in the past. Now they conveniently changed it to 92% MEDIAN SSAT. This is a very misleading number because it wont tell you the whole story. For example, for a MEDIAN SSAT of 92%, half the students can have 94% SSAT and the other half can only have 20% SSAT. The average SSAT in this case will only be 57%. On the other hand, for the same median SSAT of 92%, half the students can have 94% SSAT and the other half can have 88% SSAT. In this case the average SSAT is 91%. So the median SSAT is meaningless to gauge the quality of admits unless the average SSAT is also given. So based on the reduced number of applicants and the lower SSAT scores compared to last year, the quality of admits at Andover seems to be dropping. But as was reported, it can be spun in a positive way of reduced admit rate and reporting median SSATs as opposed to average SSATs.</p>
<p>Any statisticians out there that want to add to this analysis?</p>
<p>You are assuming that schools have the same number of vacancies every year; they dont. When schools underestimate their yield (i.e. more kids than predicted accept the offer of admission), the school reacts by shoving 2 kids into single rooms and 3 kids into doubles. The next year the school will remedy the overcrowding situation by accepting fewer kids. </p>
<p>I think MEDIAN is a more meaningful number for schools to report than AVERAGE, because median gives you are clearer idea of the middle-of-the-pack student scored, and disregards flukey data on the tails of a statistical distribution, which are just statistical noise. That is why governments use MEDIAN numbers to report important economic data like Household Income. If the state of CA reported MEAN income of its residents, then a few statistical outliers like Bill Gates & Mark Zuckerburg would skew the data and give you the wrong impression that CA residents are all rich.</p>
<p>According to my high school statistics teacher, median is meaningless as it tells you the mid-point, but it will give zero information about the actual distribution of data. For full disclosure, you need to give both numbers median and average. As per the definition of median, half the class can be 93% and the other half can be 0% or 89%. In this case in particular average is more meaningful than median, even though everyone should report both numbers even if it is inconvenient to do so. The data is already there and excel takes 2 seconds to give you the average, unless you dont want to report it. You can hide a lot of low scores from fullpays, athletes, URM this way by giving only median.</p>