A statistics professor gives a test and finds that the scores are normally distributed with a mean of 25 (out of 100) and a standard deviation of 5. She plans to curve the scores in one of two ways.

Question

1) She could add 50 points to each grade.
2) She could use the following scheme:
A: Top 10% earn A's
B: Scores above the bottom 70% and below the top 10% earn B's
C: Scores above the bottom 30% and below the top 30% earn C's
D: Scores above the bottom 10% and below the top 70% earn D's
F: Bottom 10% earn F's

If the professor uses the first method, what would the new mean and standard deviation be? Is this a fair method for curving?

If the professor uses the second method, what are the numerical limits for each letter grade?

Which method do you think is fairer? Why?

Answer 1

Just remember, under 1) the distribution is still "tight" around the mean.

On 2) 10 precent get A's, and 10 percent get F's. Did they deserve them?

Fairer? Strickly opinion.

Answer 2

Adding 50 points to each score only changes the mean. These tests are only ordinal scales.

http://www.members.cox.net/dagershaw/lol/TwoPlusTwo.html

The cutting points for grades are arbitrary and can vary from teacher to teacher and subject to subject.