Subject: ECE 260: Comments on Final Course-Grade Calculation ECE 260 Students: In the case of many students, the final course grade displayed by Brightspace reflects an alternate reality that is even further from objective reality than Donald Trump's highly-delusional perception of reality. For this reason, it is worthwhile for me to make some comments on course grade calculation in the course. Students sometimes ask how exactly I determine the final course grade for each student for submission to the University. In some cases, the motivation for a student asking such a question is to understand how rounding is used in the grade calculation process because the student is very close to the transition point between two letter grades. In other cases, the motivation is the alarm that can result from the false belief that the final course grade reported by Brightspace is correct for every student (and especially those who were excused from an assignment or exam for various reasons, such as illness). In the interest of full transparency, I will describe below exactly how final course grades are calculated. First, it is important to understand that I do not use the final course grades displayed by Brightspace to determine the grades for submission to the University. The reasons for this are as follows: 1) The final course grades shown by Brightspace will be incorrect for a large number of students because Brightspace does not properly account for any assignments or exams that were missed for legitimate reasons, such as illness or injury. If any special case handling is required in course grade calculation (e.g., due a student being excused from an assignment or exam), the course grade reported by Brightspace will be very badly wrong, and the only way to determine the correct grade is to compute it by hand using the formula on the course outline. All of the special cases for course grade calculation are tracked by the instructor in a separate document outside Brightspace (since Brightspace itself does not have any way to handle this). When the instructor indicates to a student that they have been given a special exception, this information is recorded in this separate document which is used later when the course grades are calculated. 2) The final course grade calculated by Brightspace is displayed rounded to one or more decimal places. This rounding makes it impossible to correctly determine what the final grade should be when rounded to an integer (as required by the University for grade submission). For example, suppose that Brightspace displays a final course grade of 59.5%. It is impossible to determine from this displayed grade what the correct value should be for the course grade after having been rounded to an integer (as required by the University for grade submission). For example, a true (i.e., unrounded) grade of 59.46% rounded to one decimal place by Brightspace would display as 59.5%. Clearly, a true grade of 59.46% when correctly rounded to an integer should yield 59%, not 60%. If the course grade were calculated by rounding the already-rounded (to one decimal place) value of 59.5%, an incorrect final course grade of 60% would be obtained. My workflow for calculating final course grades is as follows: 1) I prepare a spreadsheet template that can be used to calculate course grades using the assessment method specified on the course outline. This template assumes no special cases (caused by students missing assignments/exams for legitimate reasons). 2) After the final grade-change deadline for the course passes, I will export all of the raw marks for assignments, exams, and extra credit items (e.g., CMBBP and course-feedback questionnaire) from Brightspace into a file. By "raw mark", I mean the mark total for each assignment/exam (as opposed to a percentage value calculated from the mark total). The reason for using raw marks is to eliminate any unnecessary roundoff error during course grade calculation. 3) I import all of the raw mark information obtained in step 2 into the spreadsheet from step 1 and then manually adjust the course-grade calculation formulas for each special case where a student missed assignments/exams for legitimate reasons. 4) I use the course grades calculated by the spreadsheet to submit to the University. It is important to note that no explicit rounding is performed in the spreadsheet calculations until the very end. This is done in order to maintain the highest possible accuracy in the calculations. The spreadsheet first calculates the course grade as a real number. Then, in the very last step of the calculation, the course grade is rounded to an integer using the round function of the spreadsheet. If you compute your final course grade yourself in order compare with the course grade that I have calculated, it is extremely important that you carry all of the decimal places in the calculation through to the end. Otherwise, your calculation is likely to be off by plus or minus 1% (due to rounding). Lastly, when rounding to the nearest integer, there are two commonly used approaches for handling the midway case (i.e., when the number being rounded is exactly halfway between two integers): 1) unbiased rounding (i.e., round half to even) and 2) biased rounding (i.e., round half upwards). Since different spreadsheet software makes different choices in terms of unbiased versus biased rounding, I cannot guarantee which approach will be used in advance. Whichever approach is employed by the round function of the spreadsheet software will be the approach used for course grade calculation. (Incidentally, I typically use the spreadsheet software LibreOffice Calc, a free Excel clone, and I think that LibreOffice uses biased rounding.) This said, however, the halfway case is rarely encountered in practice. For example, Brightspace might say that a grade is 59.5% but one must keep in mind that this value is already rounded to one decimal place and is actually extremely likely to correspond to a value different from than 59.5%, such as 59.46%. --Michael