Question about adjusting exam scores on a kind of proportional scale

Question

Let's imagine we have ten student's scores as %

87

76

91

47

68

74

79

94

88

59

The minimum passing score is set at 70%.

The school decides to throw out the 47% grade as a hard fail.

The next lowest grade, 59 is to be adjusted to 70. An increase of 11

The school then wants to adjust the other students' scores

For example the 91% grade.

I would subtract 91 from 100 giving 9, and that gives me my adjustable range, then inside that range I want to apply the same proportional increase that the failing student got when we increased his score from 59 to 70

My math is letting me down here. I solved this problem many years ago but have since lost the excel sheet i put it in, and for the life of me I can't seem to rediscover the solution. Can anyone help with the math?

Answer 1

For the student who goes from a 59 from 70, there are 41 points that he "missed". You are giving him 11 out of the 41 points that he missed, which as a percent is 11/41 x 100 = 26.8%. Applying this percent to the student who got a 91, who has missed 9 points, you multiply that percent times 9 to see what his increase should be. To avoid rounding errors I would just keep the 11/41 as a fraction and multiply that times 9, which is 2.41.... hope that helps.