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where = German grade, = best possible score in foreign country's grading system, = lowest passing score in foreign grading system and = obtained foreign grade (to be converted into German grade). The resulting value is rounded to the next German grade (e.g. 1.6 is rounded to the German grade 1.7 and 2.4 is rounded to 2.3).
This stems from the practice that exams were traditionally given by 3 examiners. Each had to rate the student's examination performance on a 1–10 scale, and the final grade was the sum of the three ratings. On a 1–10 scale, passing is 6, so on a 1–30 scale the minimum passing grade is 3*6 = 18.
For example, if the top passing grade in a national system is attained by 30% of students in a cohort, while in another national system the top grade is attained by 10% of students, there is not enough information to compare a top grade obtained in the first system against a top grade obtained in the second system.
Grading in education is the application of standardized measurements to evaluate different levels of student achievement in a course. Grades can be expressed as letters (usually A to F), as a range (for example, 1 to 6), percentages, or as numbers out of a possible total (often out of 100).
The following tables use the German grading system. 1 is the best grade, and 6 is the worst. Former Yugoslavian students will be considered as one group in the following tables; however differences exists between different ethnic groups from former Yugoslavia when it come to educational attainment.
Another policy commonly used by 4.0-scale schools is to mimic the eleven-point weighted scale (see below) by adding a .33 (one-third of a letter grade) to honors or advanced placement class. (For example, a B in a regular class would be a 3.0, but in honors or AP class it would become a B+, or 3.33).
13 is a fairly rare grade outside of exams and requires a performance way beyond the expected. One of the reasons why the 13 scale was replaced with the 7 scale was because of the grade 13. 13s are only given to the students that have gone above and beyond the stated curriculum. To gain it you needed to know more than what was taught in class.
The Austrian grading system offers a range of five different grades (1 to 5), with 1 (Sehr gut) being the highest and 5 (Nicht genügend) the lowest grade. Students must be evaluated according to objective standards and need to earn at least a grade of 4 (Genügend) in order to pass a course.