Question

How to calculate a curved score with the following stats:

Min: 13.0
Max: 61.5
Mean: 44.48
Standard Deviation: 10.86

If a students grade was 80%, what would his new grade be?

Answer 1

Without loss of generality, we can assume that the distribution of scores are normal.

Let X be the random variable denoting the distribution of scores. Hence, X ~ N(44.48, 10.86)

Thus, (X - 44.48)/10.86 ~ N(0,1) approximately.

Let, P(X < a) = 0.8 i.e. P[(X - 44.48)/10.86 < (a - 44.48)/10.86] = 0.8 i.e. [(a - 44.48)/10.86] = 0.8 i.e. [(a - 44.48)/10.86] = (0.8) i.e. (a - 44.48)/10.86 = 0.842 i.e. a = 53.6241.

Hence, his new score is 53.6241.