Question

The instructor of a class offers his students a choice. Their final grade may be calculated in one of two ways, which they must decide on as a class. The class has a total of 500 pts available. The 29 students in the class have a mean score of 407 pts, a standard deviation of 15 and a median score of 420. Option 1 is to have the grades based solely on the percentage of total points possible in the class that a student receives. Grades would be based on typical divisions of deciles (So a student with 400 pts in the class would have an 80.0% average and receive a B- while a student with 399 pts in the class would have a 79.9% and receive a C+.) Option 2 is to curve the final grades of the class based on the Standard Normal Curve, where all those whose grades fall within 1 Standard Deviation of the mean receive a C. Those who fall between 1 and 2 standard deviations from the mean would receive either a D or B (depending on whether you are above or below the mean), and all those who are more than 2 standard deviations from the mean receive either an A or F (again depending upon whether you are above or below the mean). What choice should the class choose that would benefit the majority of students? Show all work and thought process used to get your answer.

Answer 1

Option -1: Grades based on percentages.

Mean = 407 and Median = 420. Total mumber of students =29.

That means 14 students have marks above 420, one student has marks equal to 420 and other 14 students have marks below 420.

As mean is lower than medain, long tail of low scores pulling down the mean. Means many students out of 14 (who have below 420 marks) have very low score i.e. below 400 (like 10 students). Also, on the other side of mean (right side), many students would have marks closer to mean, as such out of 14 students (who have marks above 420) very few are above 450 (like 2 students).

With this option, good number of students would have grade B (around 60%). Grade A students will be very few, might be 7 %). Remaining students will have grades C (around 11%), D (around 19%) and F around (3%).

Option -2 : Grades based on Standard Normal Distribution.

Mean = 420 and Standard Deviation (SD) = 15

As it is standard normal distribution,

2.28% of students => marks above 437 => A

13.59% of students => marks in range 422 to 437 => B

68.26 % of students => marks in range 392 to 422 => C

13.59% of students => marks in range 377 to 392 => D

2.28% of students => marks below 377 => F

Class should choose option -1 as it would benefit the majority of students.