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How to Scale or Curve the Grades for an Examination?

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How to Scale the Grades for an Examination?

I am the teaching assistant for a course in economics, and one of my responsibilities is marking examinations.

I had just finished marking the midterm, and the grades were very poor. The details are (approximately):

Mean: 23%
Standard Deviation: 5%
Min: 4%
Max: 68%
Number of Students: 84

Upon consultation of the professor, I was told to scale the grades. The method he had given me was to add a fixed amount to each student's grade such that the mean would be 72%.

To me, this seems to be an inadequate way to correct the distribution of grades and would be unfair to the students who did score much higher than the class mean.

My question is, what is the best way to rescale the grades for an examination such that the it is fair to all the students in the class?