給分膨脹問題

1、成績給分問題的膨脹數(shù)學(xué)建模導(dǎo)論第二次小作業(yè)2012.12.11作業(yè)中主要問題：作業(yè)中主要問題：1. 沒有清楚回答題目中提出的四個問題，部分同學(xué)只提出了方案。2. 假設(shè)不合理，例如所有同學(xué)選擇的課程相同。3. 很多同學(xué)提出的解決方案都是按照學(xué)分加權(quán)平均，按照學(xué)分進(jìn)行加權(quán)是否合理？(課程難度、課程數(shù)目)4. 很多同學(xué)沒有對所提出的方案的有效性進(jìn)行驗證。 Combining student grades using simple averaging to obtain a GPA score results in systematic biases against students enrolled

2、 in more rigorous curricula and/or taking more courses. Here is an example of four students in which Student I always obtains the worse grade in every course that he takes, yet Student IV always obtains the worst grade in every course that he takes, yet Student I has a lower GPA than Student IV does

3、. The problem is to determine a “better” ranking than one using pure GPAs; this problem has no simple “solution.”Specific items that the judges looked for in the papers included:Three criteria: simple fair (account for the quality of students) logically consistent (an example)Main idea: One approach

4、 is a system of quality points bases on comparative performance within each course. In this system, a students quality points for a given course can be calculated based on performance relative to students overall performance in the course. Overall course performance may be measured by the mean or by

5、 the median of all the grades in the course. The students individual performance can be measured in terms of standard deviations from the mean/median.The ModelThe question of using mean or median as the standard of comparison is of utmost importancethe mean is the preferable estimator for data resem

6、bling a normal distributionthe median is robust to outliers or extreme observations（有些同學(xué)直接用學(xué)生分?jǐn)?shù)減去平均分作為新的分?jǐn)?shù)） 敏感性分析略Strength and weakness: simplicity fair doesnt account for the quality of students within a class. There are many courses known to be popular by top students. consistencySuggestion for th

7、e model median may be uninformative trimmed mean（切尾均值） a robust estimate of the variance interquartile range (IQR) (四分位距)Introductionan acceptable ranking method :reward students for scoring welltaking into account the difficulties of coursesclearly distinguish the top 10% studentspreferably, well-r

8、oundedness (全面發(fā)展)least-squares method: not very sensitive, intuitive, well-roundedness difficult to computeIterated Adjusted method: easier to calculatestandardized method: doesnt properly correct for course difficultyplain method： all courses are graded on the same scale, too many tiesClass, course

9、 doesnt sufficiently distinguish between students (the average grade is A-, all above average students within any class receive the same grade, A) does not correct for course difficulty, thus punishes both the students taking a difficult course and the instructor teaching it encourages specializatio

10、n by studentsWe determine how many standard deviations above or below the mean each students grade is. This method is a non-robust version of the method in the first paper.Strength not much difficult to calculate than the plain method Each course can be considered independently do correct for differing course averagesWeaknessesin it.This method systematically corrects for instructor bias in giving grades, thus eliminating the tendency of students to select easy courses.This algorithm tends to “punish” students in courses where grades are unusually high. Maybe the high g