snotrocket wrote:tl wrote:For Fall 2008, the median GPA for 1Ls classes was 3.23. First, I don't see how then the median GPA for individuals will be a 3.3 when the exact same data is used (it's just grouped differently). However, I'm not an expert at statistics, so I'll assume that that can happen. Upperclass Courses median GPA was a 3.46. Seminar median GPA was a 3.67. There are way more upperclass courses and seminars than 1L courses. When you apply that difference over 4 semesters, is it even statistically possible for the median GPA to only go up .04?

You have to keep in mind the difference between mean and median. The grading guidelines and the report you linked deal with the target and actual

means and do not consider the per class or cumulative medians. We can just take the grading guidelines and construct a distribution of grades using them to see why this matters.

Figure that the class has 100 students and the professor grades precisely according to the specified curve (see table below). The arithmetic mean for the class will be 3.19 -- right on target. But the median is the grade that falls in the middle of the list of all grades assigned, sorted from highest to lowest. Because we have an even number of grades here, the median is the average of the two grades that straddle the exact center -- positions 50 and 51. Both grades in those slots are B+, so the median is 3.30. Another measure of curve shape is the mode, or the value that occurs most often. Here the mode is also 3.30/B+ (30 out of 100 people receive this grade). This situation -- where the median and mode both fall higher than the mean -- is the definition of a curve that is skewed to the left (meaning it has a fat upper end and a long skinny left tail). This is a typical shape -- by design -- for grading curves at all top schools.

So, if we had 100 students and they all took one class graded according to the specified curve, it's not only statistically possible, it's statistically inevitable that the mean will wind up at 3.19 and the median at 3.30. Classes vary somewhat, and the mean of means (reported in the document you linked above) lands closer to the high limit than the target. But even if all classes go high on the curve, this will not move the median much, if at all. And even though not all people will get the same grade in all classes, the curve in each class is a zero-sum game, so anyone doing better in one class will correspond with someone else doing worse. Overall, the distribution of cumulative GPAs for the entire class of ~360 people will fall right in line with the target curve followed by the individual classes, so the overall distribution will have the same character noted above -- fat upper end and long, skinny left tail, with a median and mode noticeably higher than the mean.

As far as the increases between 1L and upper class GPAs go, again you have to keep in mind the difference between mean and median. A big change in per class or cumulative means might move the median only slightly or not at all. This is in fact one of the reasons for using these measures of central tendency together -- the median is generally more stable and less responsive to outliers and changes in the shape of the distribution compared with the mean. Even if we assume a far softer curve, say with 20% A+/A, 25% A-, 40% B+, 15% B, and nothing lower, the mean will shift dramatically to 3.50, but the median will still be 3.30/B+ just like before. So a modest upward shift of 3.30 to 3.34 seems right in line with what we would expect, given that the median shifts far less than the mean, and that, as noted above, the bulk of credit hours (not classes, but total credits taken) still have to fall in according to the grading guidelines.

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