# What is the mean in an standard exam? (For grading on a curve)

Suppose a grading system is used in which grades vary between 1 and 100. Grades below 50 are failing grades. If I want to grade the students on the normal curve, which grade should I choose as the mean of the distribution? In other words, what should be the mean of the new grades? The number 50 is somehow counter-intuitive, as it results in half of the students failing the exam.

Note: This question was previously posted to stats.SE, but was voted as off-topic there.

• Grading on a curve sucks. Feb 15 '18 at 14:50
• The whole concept of grading on a curve seems wrong - it means paying no attention to how good students are in absolute terms, and only how they compare to each other within a given class. Why would one want to do that? Feb 23 '18 at 0:18
• @Flyto. Good point, but in the case of a very difficult exam, grades are indicative of absolute performance only indirectly (if they are so at all, in that case). I mean they are only proportionate to the absolute (objective) performance. Feb 23 '18 at 10:06

“Grading on a curve” means that you select what percentage of grades you want to correspond to a given final grade. It’s entirely up to you how you choose the resulting mean grade using that system. If you want to make the mean a 60 or an 80 or anything else, that’s your call. Ultimately, though, the point of the curve is to avoid having “grades less than 50 are failing.”

• Thanks @aeismail, BTW What is usually done on this respect? Feb 15 '18 at 17:19

Your last sentence tells me that you do not want a normal distribution to be your "curve" since, in the symmetrical distributions, the mean and the median coincide. In reality, in my experience, the distributions of students' performance are more a right skewed (right tail long) chi square distributions. These distributions of course depend also on the difficulty of the exams and how instructors tamper with the examination procedure. In cases of those who want to pass the whole class you may see chi square distribution drastically skewed to the left, where, like in lake Wobegon, "all students are above average". That much for the distribution of students' performance. Grade "curving" does not have much to do with these distribution curves, rather has to do with the ranking of the students and instructors (or sometimes implicitly or explicitly departments') manipulation of grade or passing percentages. So "curving" amounts to drawing segments on the ranking score line and assigning appropriate grade labels, arbitrarily, with one restriction that hopefully higher grades imply higher overall class score...

• Thank you @Rado. Regarding your first sentence, isn't a normal distribution with mean 50 as symmetric as one with that of 70? And would you please explain this part ranking of the students and instructors (...) manipulation more? Feb 15 '18 at 17:58
• @Kaveh When you talk about percentage of students below certain point, you are talking about a percentile. When, like in your case the number is 50%, you have the median. The mean is not to do with percentages. In symmetrical distributions the mean and the median coincide...
Feb 17 '18 at 3:18
• @Kaveh Many instructors and schools manipulate exams and then the resulting scores to get passing grades for as many students as possible. This applies to measly community colleges to Ivy League Universities, with a negligible number of exceptions.