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Exam grading FAQ.md

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Exam grading FAQ

There seems to be quite a bit of confusion on how the core Purdue calculus courses (Calc 1-3) are graded. Here I try to explain how exactly it works. This is for Calculus 3 (MA261), but the ideas are the same for many others (like Calc 1/2).

For Spring 2020 onwards

Here, your grade is computed by adding all components: exam, quizzes and HW, and then the cutoff is centrally determined. This is much like any other course that you'll have experienced.

Purdue is offering a guaranteed curve, and this is your total score - including HW, quizzes etc. This means that you will be sure of getting that grade if you can hit that minimum score, irrespective of other factors, and the case of you losing a grade because someone else beat you in recitation cannot happen. This does not preclude the curve being more generous than this,

Step 1 - The exams

The process starts with the exams. In Calculus 3, there are two midterms (each out of 100) and a final (out of 200), for a total mark out of 400. This is the only metric used for the initial ranking process. The instructors first determine the mark cutoff for each grade (eg: 335/400 for an A). Then, they rank all the people based on only their combined exam scores.
For Calculus 3, out of the ~2400 students, roughly 20-23% people (around 500 - 550 students) will get an A - some of them with an A+, and some with an A-.

Step 2 - The recitation (Before Spring 2020)

Now the grade cutoffs have been determined and a 'grade' has been attached to your name just based on your exams. Then your recitation instructor will look at their students, and take your exam-only grade, and add it into a 'basket'.

As an example, for a recitation of 30 students, assume that 7 students have an A, 7 have a B, 7 have a C, 7 have a D and the remaining poor two students have an F. So the recitation 'basket' contains seven As, seven Bs, and so on.

Step 3 - Getting your final grade (Before Spring 2020)

Now that the recitation 'basket' is done, then your quiz and homework scores are added, and then all students in that recitation will be re-ranked, this time with your entire score (out of 550). Then, he'll take the grades from the 'basket'. This means that while they (should!) love all of you and would like to give all their students As if they could, their 'basket' contains only a finite number of As (in this example 7) and hence can only give that many students that grade.

How does that matter in my final grade?

It depends. Assuming a normal Gaussian distribution, it's unlikely (assuming that you've been doing your homework and have obtained a reasonable quiz score) that if you're doing well above average, that your grade will be impacted. This is because assuming a homework score of 100, the difference between your classmates' scores will be a few points at most. This goes the same way if you're well below average - doing well in quizzes will be unlikely to save you.

However, if you're around the median, this could impact your grade, as many of you will be bunched around the C to B region. So considering that many of you will get similar total exam scores, the quiz and HW can make or break a +/-. A even tougher scenario is if you're in the A-/A (or any two grades') border (which is possible due to the cutoffs this year) - one point can literally decide between A and A-. Yikes.

Example? (Before Spring 2020)

Sure. If two students (let's call them Student 1 and 2) have the same exam score of say 260/400 (which could be a C) and another with a score of 250/400 (which can be a C-). Now, let Student 1 and 3 have a quiz+HW score of 145/150, while Student 2 slacked off and got only 125/150. Then the recitation instructor adds up their scores. So,

Student 1's total score: 260 + 145 = 405/550
Student 2's total score: 260 + 125 = 385/550
Student 3's total score: 250 + 145 = 395/550

The recitation instructor now looks at their scores. He has two Cs and one C- to give out. Even though Student 3 did a bit poorer in the exams compared to Student 2, the fact that Student 3 did well on the homework and quizzes meant that he overall did better than Student 2, and hence gets the C. Student 2 is hence consigned to a C- (and rues themselves for not doing their homework).

Part 2 - Getting your final grade

A lot of this information was originally written for the Fall 2019 information, and much of the cutoffs (unless other mentioned) is for that cohort. Again though, this should still be helpful for future semesters.

I've added this section in response to several queries on the GroupMe chat.
First, go to MyMathLab and click Gradebook:

Opening Gradebook

Then you can find your total score by multiplying the final 'points earned' score by 5.5. Doing that, we see that Leaderboard has (85.27) * 5.5 = 469.8 points. Will he get an A? Let's hope he does. (update: he did!)

Below are my answers to some FAQs that I've seen:

My "Final Score" is a 0, but my "True Final Score" is something else.

Don't worry. You haven't done the impossible and scored a zero. Your actual score is the one reported by "True Final Score".

Quizzes 12 to 14 are zeros, despite my never taking them.

MyMathLab was originally set to have 14 quizzes (don't ask me why), but we only had 11. So what they did in essence is fill quizzes 12 to 14 with zeros, and then drop the lowest 6 quizzes, consuming the three zeros in the process. The three quizzes you didn't take are marked as (omitted), and the three quizzes that you score the lowest are marked as (dropped).

If that isn't the case (i.e, your three lowest actual quizzes haven't been dropped), talk to your TA.

What's my actual HW score (/100) and quiz score (/50)?

Divide the points that you got in that section with the category weighing, and multiply by 100 or 50 as required. Or use the average scores category.

In Leaderboard's case, he got 18/18 (100/100) in the HW, and 8.27/9 (45.95/50) in the quiz.

I got score X. What's my grade?

Fall 2020 data (source). Grading policies are somewhat different this time, in particular the quizzes are course-wide, and hence recitation-based variances do not apply.

Grade Percentage
A+ 95
A 90
A- 87
B+ 84
B 80
B- 77
C+ 74
C 69
C- 65
D+ 60
D 55

The below is Fall 2019 (and before) and is provided as an archive.

As said before, it depends on your recitation. However, thanks to a couple of TAs who have kindly provided their grading cutoffs, we can make a very good estimate on what grade you could get. Credits to Ray Wu and Jake T for kindly providing them from the GroupMe chat

Grade Junpyo Choi Duo Cao unknown Fall 2018 unknown Fall(?) 2017
A+ N/A 502 522 495
A 463 470 485 458
A- 436 439 470 433
B+ 413 421 448 413
B 396 397 428 390
B- 377 379 407 374
C+ 361 N/A 389 356
C 343 348 363 335
C- 305 310 341 316
D+ 278 278 333 300
D 261 263 281 277

Anyone below the minimum for a D gets a F.
What does this mean?

  • If you are in Duo Cao (not sure which section) or Choi's 10:30 am section, then you can determine your actual grade from that table.
  • If you're in any other recitation, then you can use this table to make a very good guess on what your final grade would be. In our case, Leaderboard has a 470, so he can safely, but nervously, say that he has an A. It depends on how 'hard' your recitation was in terms of quizzes. Also see the exam-only cutoff below.

My exam score was X. What was the grade assigned to my name just based on that?

Credits to Matthew Graber

You can use this table to find your grade based only on your exams:

Grade Cutoff (/400) Percentage
A+ 380 (?) 95
A 323 80.75
A- 291 73.75
B+ 273 68.25
B 253 63.25
B- 236 59
C+ 217 54.25
C 194 48.5
C- 164 41
D+ 151 37.75
D 128 32

I had said in the past that your grade cannot be adversely affected if you had lost 8 or less points in the sum of homeworks and quizzes. These cutoffs show that that's not fully true. The reason is that you could have received a score of 322 or 321 or 320 (out of 400) if you had 'bombed' the final and nothing else (that's because each final exam point is one more than each midterm exam point). If you are in that situation, hang on, as your quiz and homework scores would suddenly make a huge difference - the difference technically goes down to 1! Similarly, those wth 323 (like Leaderboard) or even 324 exam points cannot rest that quickly - depending on your situation, you might end up unlucky and drop a +/-.

I'm only X points away from that cutoff. Will I get that higher grade?

Technically not, as they only have a finite number of each grade to give out from the 'basket'. That being said, TAs could be willing to round up your score, and also probably raise your grade if you are that close (say 1 - 3 points). I can't tell what your result would be, but Leaderboard hopes that you get the better grade!

I think I will get only a D+ or a D. Will I have to retake?

Technically it depends. Most people will have to unfortunately. That's because while technically 'sufficient' for the purposes of getting credit, you will not be able to take MA265 or MA266 or take anything else that has Calc 3 as a pre-requisite , as you need a C- in that case. This includes nearly all Engineering and CS students. If you're in FYE, this may also cause issues with satisfying your academic requirements.

If you have a C-: Some courses like CS381 (which is required in some tracks and a very useful course overall) require you to have a C in MA261. C- would not satisfy the requirements in this case. However, you can still take MA265, but bewarned that you cannot go back and retake MA261 should you decide you want to take CS381 later.

I've passed MA261! Will my next math course be like this in terms of grading?

Well done! The answer depends on which course you're taking next.

  • If you're taking MA262, then both midterms and the final are course-wide, and hence the only thing controlled by your instructor are the homeworks (especially handwritten) and the quizzes. Hence you're still going to have a similar experience in general, for better or worse, though the percentage that's graded by your instructor is 16% and not 9% as in MA261, so there is a greater chance that it'll make a difference to your grade.
  • If you're taking MA265 or MA266, then only the final is course-wide, with the midterms being instructor-dependent. This means that the percentage that can be instructor-graded becomes as high as 65% (or 45% in MA 266). This means that the homeworks and midterms can make a larger impact here, and it is no longer possible to accurately determine your final grade solely from the course-wide final.
  • If you're taking a 300-level math course such as MA351 or MA366, then nothing is course-wide (not even the final) and everything will be instructor-dependent.