Very often, at the end of an exam that seemed particularly difficult, students will ask the professor, "Are you going to curve the grades?" Unfortunately, "curving the grades" doesn't necessarily mean that you will receive a higher grade on a test, although you might like to think so! Curving grades is actually a technique whereby a fixed proportion of the highest grades receive As (even if the highest grade is a failing grade on a percentage basis), and a fixed proportion of the lowest grades receive Fs (even if the lowest score is a passing grade on a percentage basis). The B, C, and D grades are also assigned according to fixed proportion. One such allocation uses the following proportions.

1. If the average C grade is centered on the average grade for all students, and if we assume that the grades are normally distributed, how many standard deviations on each side of the mean will designate the C grades?
2. How many standard deviations on either side of the mean will be the cutoff points for the B and D grades?
A histogram of the grades for an introductory Statistics class together with summary statistics follows.

For ease of calculation, round the number of standard deviations for C grades to ±.5 standard deviations and for B and D grades to ± 1.5 standard deviations.
3. Find the cutoff points for A, B, C, D, and F grades corresponding to these rounded values.
4. If you had a score of 92 on the exam and you had the choice of curving the grades or using the absolute standard of 90-100 for an A, 80-89 for a B, 70-79 for a C, and so on, what would be your choice? Explain your reasoning. Is the skewness of the distribution of grades a problem?

Transcribed Image Text:

Letter Grade Proportion of grades 10% 20% 40% 20% 10% Histogrum of Grades 50 30 10 30 s0 60 Grades 40 70 80 90 100 Descriptive Statistics: Grades Variable N N M StDev Minimu Q1 Median Grades 290 0 79.972 12.271 31.000 73.000 82.000 88.000 100.000 Mean StDev Minimum 03 Maximum