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I am seeing the relative grading structure of few of the institutions. The formula they follow for grading is as follows.

For a large batch of students:

  1. they take the final marks of students
  2. Calculate the mean marks
  3. Calculate the standard deviation of marks
  4. Then for those students whose marks are greater than mean + 1.5* standard deviation are assigned A+ ( the highest grades).
  5. those students whose marks are less than mean - 1.5* standard deviation are assigned F( failed).

My question is if the distribution turns out to be symmetric around mean (like Gaussian), will it not be true that there must be some students that will fail mandatorily.

I may be wrong but I find this concept quite absurd and amusing. Can someone help me with this? I have many times seen in class having relative marking all the students to pass, how this is achieved or the distribution is not symmetric there?

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  • 1
    What if no student has a score less than 1.5 standard deviations below the mean?
    – GoodDeeds
    Jun 18, 2021 at 21:21
  • @GoodDeeds If I say that none of the student has got less than 1.5 of standard deviation then I am saying that distribution is asymmetric. However, in a large class distribution should more or less follow Gaussian or for that sake if I take any symmetric distribution then suppose I got 10% students A+ grade is it possible then that no student will fail?
    – Userhanu
    Jun 18, 2021 at 21:32
  • 6
    My experience, even with large classes, is a bimodal distribution... the students who get it and the students who don't. In such a distribution, the mean is not really a useful measure of central tendency.
    – Bob Brown
    Jun 18, 2021 at 22:03
  • 2
    @Userhanu Not necessarily: every student getting the same mark also gives no students below -1.5sd. I also see no reason to expect the distribution to be anything like symmetrical. Comparing the data here and here (PDF) for 2019 (since 2020 exams didn't happen), many subjects look very asymmetrical. Jun 19, 2021 at 17:59

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