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 6.5 standard deviations and for B and D grades to 61.5 standard deviations.

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.

Transcribed Image Text:

Frequency 50 40 30 10 22 20 Histogram of Grades 0 30 40 50 60 70 80 Grades 90 100 Descriptive Statistics: Grades Statistics Variable N N* Mean Grades 290 0 79.972 0.721 SE Mean StDev Minimum 12.271 Q1 Median 31.000 73.000 82.000 88.000 Q3 Maximum 100.000