4 curves to save your math grades

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A lot of math teachers in Taiwan will take the square root of students' exam scores and then multiply by 10 to "help" the student pass their math exams, but why?! While I can only give you a math reason why it would help the student, I do not know why they choose to "curve the exam" like that. Thus, I will give you three more ways to "curve the exam" to help students pass the class. Let me know which way you like the most!
PS. As a calculus teacher in college, I do not do any of these : )
0:00 What does "can you curve?" really mean?
0:56 Check out DataCamp to learn about data science
2:34 1st curve: 10sqrt(x)
6:28 2nd curve: x+15
8:29 3rd curve: normal curve
11:49 4th curve: 20% of each letter grade
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[@blackpenredpen]

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[@happyhippo4664]

In my Differential Equations class, apparently the class wasn't doing so well. So the professor said he would add 10% to everyone's score. Since I got 100, by new score was 110. So I benefited the most!

[@paolo6219]

How did you get 100 in diff eq🤯🤯

[@blackpenredpen]

Very nice!!

[@samsonblack]

And in a different sense (relative change Δx/x = 10/x) you benefited the least! 😬

[@nickfair2317]

@@samsonblack wouldn’t relative change be the same for every grade? (1.10x-x)/x = 0.1x/x = 0.1

[@reidflemingworldstoughestm1394]

The OP's method, and setting the highest score as 100% (or, say 97%) are what I think are the fairest ways to grade on a curve.

[@assaf127]

In some tests, you could get a negative score if you answered wrong on some questions. We joked that using the square root method would result in imaginary scores

[@blackpenredpen]

That will be 😎

[@happyhippo4664]

I won first place in my high school statewide math test that way. There was a difficult problem that I skipped. My friend answered wrong. In that test, a wrong answer was penalized more than no answer.

[@furiousmonkey1049]

Imagine going home and telling your parents that you got 10i on your test

[@dawsonbauer9900]

My favorite part is where he says "and the way you compute standard deviation is by plugging it into a spreadsheet and using it to compute it" I was legitimately rolling laughing. This man has felt the pain of calculating that by hand and it is never worth it!

[@rakiston]

The professors I had would use the "add X points" method, but the X would be determined by what was needed to give the highest scoring person a 100. So if someone already got a 100, too bad, no increase. But if the highest person scored 60, everyone got +40 points!

[@blackpenredpen]

😆 I kinda like that!

[@doublej1076]

I like that one too, because it takes the professor's ability into account (kinda). If the best student in the class can only get a 60, especially in a lecture-hall class with 200 people, that's more the prof's fault than the students'.

[@jeffreyh.1436]

My environmental science teacher does this, and I don’t really like it because it is prone to outliers. However, I suppose it does shift the curve well if there are no outliers.

[@weirderrichard4u]

What if everyone didn't take the test, would everyone then get 100%? 🤔😂

[@vaxjoaberg]

​@@weirderrichard4u I doubt I'll find it but I clearly remember reading an article about a class that did exactly that. They had a similar sort of grading scheme so the students got together and made a pact to all get 0s on the final test. As I recall, the instructor capitulated and gave them all As.

[@auser9791]

My teachers usually use method 2B to curve, instead of adding points to everyone's score, they reduce the total score by some value. So instead of 28/100, you'd get something like 28/90. This basically changes the slope of the grade function, which causes good grades to profit more than bad grade. The original 28 would be at a 31.1 (+3.1), the original 77 at 85.6 (+8.6). And it aligns well with the perception of students. Instead of "y'all get extra points", it's an "this problem was too difficult, it's point are not part of the maximum score, but any answers still give credit" tl;dr: reduce point total, students get extra credit based on their demonstrated ability instead of a flat number

[@landonponek5729]

The version of this that I've seen is to just subtract so that the highest individual score will be 100%.

[@christianstonecipher1547]

I had multiple math classes in college that also curved this way. Usually it was a matter where you were not expected to finish all the questions so to get full points you had to say correctly answer 4 out of 7 questions or something like that to get full points. It only differed in whether you were allowed to get over full points and whether or not the teacher even allowed you to answer every question or if they just told you to only write answers for x questions and if you wrote an answer for more than that then they would only grade the first x answers.

[@GeldarionTFS]

This is my preferred method in my classes.

[@garmo1968]

This is what I know... in the videos sample numbers instead of being 96 out of 100 points, all grades are now out of 96 points... if you give a brutal test that everyone fails and the highest score is a 50 then everyone's percentage score doubles and that's on you for not conveying the material better or not setting up the test environment properly (maybe not enough time), or maybe the students unionized and agreed to all get the same score

[@tibees]

Really interesting topic! I never knew there were so many methods used for this.

[@blackpenredpen]

Thanks! These are the ones I have heard of. Apparently there are a lot more ways to curve that the viewers are telling me. I am amazed! 😆

[@blackpenredpen]

@[MW]Cole in this example I would have to add 20.3

[@manla8397]

The last one will guarantee someone certainly fail their exam even if everyone already did well (say 90+). Moreover the side effect is that students will try to compete each other instead of helping each other. Say if one bright student figured out a trick how to do a difficult question, in order to get a high score, he will hold this method himself instead of sharing out to his peers. This is the last thing, a teacher want to see especially in a university. Method 2, also have some faults. +15? Where this number comes from? It seems it is a bit arbitrary. Some students may argue that they are the marginal case. It is not fair and not scientific. They can question your judgment. Using standard deviation is more scientific. However, if the sample is large enough, this will guarantee someone will fail. Method 1 is a genuine method. The one who got 100 will always got 100 and the one who got zero will always got zero. At the end, no matter which method, it is totally depends on the data set itself.

[@danielnewby2255]

The psychology of curved grading is the same as brackets though, and this exactly shows that. Students in the top percentiles are tacitly encouraged to degrade the performance of their peers, across the entire student body, so that they're in the +2 SD rather than having the average pushed beyond what's attainable.

[@rocketcrazy3467]

My teacher would give everyone extra credit, but only enough to make at least the top 20% (sometimes less though, depending on how the unit went) of the students have A-'s. This way there was still a way to get more than a 100 and lower scoring students (though not extremely low) could still make it in the class while making it fair for everyone. I liked cause the bonus wasn't arbitrary though I got some flack from my classmates for making it difficult for them to get a big curve.

[@MrRogordo]

I just don't get the normal curve method they show here. It's completely unfair. What my teachers used to do is get the real normal curve and then displace everyone's grade to a normal curve with mean something like 10% extra of the passing grade. Cause we don't have the letter grading system and the credits are the real grade, this way cancels the negative outcome and it's consequences on student behaviour. EDIT: Obviously is a flat value added to everyone, but it's more scientific than just adding X because whatever. They were saying that the average student should pass the course, what we expect as teachers

[@Mosk915]

A professor in college I had for a large accounting class had a distribution with a specific mean and standard deviation that he wanted for each exam. All the scores would be scaled so that the distribution was achieved and the grading scale was still the normal 10% increments. If anyone’s raw score was higher than their scaled score, they got to keep the raw score. I guess this is essentially a combination of methods 2 and 3.

[@pokemonjourneysfan5925]

Michael, have you ever heard of parasitc numbers? An n-parasitic number (in base 10) is a positive natural number which can be multiplied by n by moving the rightmost digit of its decimal representation to the front. Here n is itself a single-digit positive natural number. E.g. 4*128205=512820, so 128205 is 4-parasitic. Most authors do not allow leading zeros to be used. So even though 4*025641=102564, the number 025641 is not 4-parasitic.

[@jeezuhskriste5759]

@@pokemonjourneysfan5925 Ok? Does that have anything to do with the comment?

[@pokemonjourneysfan5925]

@@jeezuhskriste5759 Well, kind of. it's math related. Plus i thought it was fun to talk about parasitic numbers.. Challenge for you, find a 5-parasitic number.

[@adolfohenriquez6715]

@@pokemonjourneysfan5925 copypasted from wikipedia?

[@binary_gaming113]

The most important thing is that it should not make the final grade of anyone worse, especially the ones barely passing and the ones going for an A

[@Roescoe]

So you're telling me the normal distribution is bad? :P

[@NWRIBronco6]

@@Roescoe Yeah it wicked is in this example. A had to be >100 to start, an impossibility. 😆

[@Roescoe]

@@NWRIBronco6It's the ultimate "everyone gets a trophy curve" hence why it's so popular on a poll BPRB made

[@clayton97330]

So... The square root method just uses a 81 64 49 36 scale instead of a 90 80 70 60.

[@Hi_Brien]

Yup- they're not gonna make grading hard for themselves lol.

[@blackpenredpen]

Pretty much.

[@quasar_catfish]

One type of curving that I really liked was the "cushion" method. For the example data in the video, the highest score was a 96, so every exam would be graded out of 96. So the 81 would turn into 81/96, which is about an 84.8.

[@thomasrad5202]

Doesn't work for engineering classes because you can't divide by 0

[@blackpenredpen]

Ah, I forgot about that one!

[@reidflemingworldstoughestm1394]

@abigmonkeyforme If you usually get the highest score and it's in a small range, say 94-97%, and because of some bad test designs you (along with everyone else) score well below normal, the OP is the perfect method, but arguably with your current score now representing your typical 94-97%, rather than 100%. Now, if the problem you laid out above begins to play out, and you start getting below your typical range, against both the test and the rest of the class, the instructor will be aware of this and can adjust the curved top score accordingly. Another problem with your scenario is that it isn't often going to be very easy to shoot low without going below the next highest score, and giving up points two ways. I only recall one instructor grading on a curve, and that was because his approach to test writing was rough to say the least. Come exam day the whole class was edge, except for me because I knew that he was going to grade on a curve and we'd all score in the same range we normally would have if he hadn't dropped in bomber questions that didn't even look like the material we'd covered, or took 20 minutes of algebra to set up the integral.

[@reidflemingworldstoughestm1394]

@abigmonkeyforme " Mine are based on experience of spending the past 30+ years with college students. I'm very aware of what they can do, given the opportunity." I think your arguments are based on your interpretation of what you see, and are probably nothing more than a conclusion you reached before you even saw the evidence. I mean, if your argument relies so heavily on an appeal to authority, how can we trust your ability to read student behavior correctly, or even be honest? And besides that, your argument sidesteps the instructor's ability to adjust to your interpreted scenario -- not to mention that it requires overuse of grading on a curve, rather than only using curves when bad test design merit it. There isn't a fairer way to use a grade curve to compensate for bad test design.

[@reidflemingworldstoughestm1394]

@abigmonkeyforme Ah, that appeal to expert again... so handy when you don't have any legs... And you're skipping right over interpretation and pretending that it's observation. Of course you've seen a lot. Every body has. How much you've seen isn't in question. It's your interpretation that is in question. "I appreciate you wanting to share your opinion of my "argument", but I'm not interested." The funny thing about that is your inconsistency, seeing as how you led off with your opinion of my my argument. More than once. I have to wonder why you think you can do it but I can't. Frankly, between your hypocrisy, your appeal to authority and your ad hominem ignoring my arguments because I haven't claimed the same experience you claim (again, not relevant), you come across as not having much in the way of cogent support for your claim about the proper use of grading on a curve. Other than having simply pulled your idea from nether regions, there isn't a single a reason for you having given the last shred of your credibility the old heave ho.

[@sagoot]

I have heard of a test where every wrong answer deducted points (starting at 100). The class didn't do so well, and so they decided do add the square root of the score to everyone's score. However, someone had gotten a negative score and so he evntually ended uo with a complex score!

[@dudono1744]

nope, at that point you break the whole scoring system since it's neither above or below passing grade. and if you can reach -100 and take magnitude, you're above 100

[@binary_gaming113]

The last way is just stupid because a fixed amount of people will always fail, even if everyone is in the original B-A range :(

[@bobsmith2062]

The number of fails doesn't increase after applying the method. It went from 5 fails to 2 fails. You would not use this 'curve' if the number of fails increases.

[@vaxjoaberg]

@erazorblade's point is that if every student scored above 90 (out of 100), normally resulting in all of them getting As, some of them would nonetheless find themselves with a failing grade once that last "curve" method was applied. If the instructor is deciding which curve to use after the test is finished and the scoring is done then why bother using an algorithm at all. Just give each student whatever grade you feel they deserve. Give everybody an A and go out partying.

[@MikehMike01]

In my university, they used the last method but not even percentages. 30% A 30% B 30% C 5% D 5% F

[@stephenbeck7222]

You should look up the Kennedy scale method and read Lin McMullin’s thoughts on test difficulty at his teaching calculus blog. The reality is that all tests have a curve baked in based on the effectiveness of the course instruction/assignments (maybe you use examples that are closer to exam material) and the difficulty of the test (maybe you use more ‘hard’ questions when you write the test). Unless your test is all multiple choice, there is also a subjective element to the grading of the exam itself that adds to the curve.

[@Julius314159]

Don't forget the curve that's "baked in" based on the magnitude of student effort.🤭

[@Happy_Abe]

The reason for the 10 times the square root of the grade is because it has nice curving properties. It keeps a score of 0 at 0 and keeps 100 at 100 and all grades in between get improved. It’s also a continuous nice curve so it feels less arbitrary than other curves There are whole families of curves that behave like this but this one is one of the least exaggerated ones. For example 100^2/3 times the cube root of your grade will also have this property but the curve will be very drastic

[@ffc1a28c7]

Anything of the form x^k/100^(k-1) will curve it to some degree of k. k=1/2 is the 10sqrtx, k=1/3 is the cbrt(10000)cbrtx, etc.

[@Happy_Abe]

@@ffc1a28c7 yes, but as k gets smaller, the curve becomes more exaggerated and converges to a jump function where it’s 0 at 0 and 100 on (0,100] in the limit as k approaches 0

[@ffc1a28c7]

@@Happy_Abe that's the point of it being a parameter. It allows you smoothly curve anything, to any degree.

[@Happy_Abe]

@@ffc1a28c7 yup

[@Hazel.Autumn]

I had a couple professors who would just go with the normal curve method, BUT, they would make it so the curve couldn't hurt you. If everyone else scored really well and got >80 and you scored a 71, your grade couldn't be lower than a C-. That little safety rule made a lot of students more comfortable.

[@Tyeewhyee]

When I’ve curved in the past, I’ve usually used a variant of method 1 (where I take the square root and multiply by 10, or something similar). At the college I worked at, the exam averages were routinely in the 30% range, so it helped bring the scores into a more “reasonable” range (with the bigger boosts for students near the exam average)

[@danielnewby2255]

If you have scores that are that outside the normal linear range there's either something wrong with your testing / scoring methods, the instruction, or it actually starts to make more sense to use the standard curve across your entire student base.

[@maxxetto8124]

@abigmonkeyforme or the instructor didn't teach well enough/gave the right material for the exam. Often making examples too close to the material is wrong, but carefully tweaking them and understanding how to tweak them for a difficult yet achieavable exam is a skill not all professors own.

[@Majestic469]

My IB math HL teacher in high school used the square root curve, and I loved it

[@landsgevaer]

10sqrt(x)=sqrt(100x)=geomean(x,100) It is the geometric mean of the original score and 100. So it "pulls" the original score towards 100.

[@blackpenredpen]

Ahhh, that makes so much sense now!!

[@blackpenredpen]

Wait! What if we do (x+100)/2? haha! So interesting!

[@landsgevaer]

@@blackpenredpen or 200x/(100+x), the harmonic mean; possibilities are endless for a mathematician...

[@adamant8435]

I hope by mum watches this video. She always gets mad by looking at the scores of my exams, doesn't doesn't take into account the overall performance of students

[@janAlekantuwa]

I like the square root method the best (we call it the Texas Square Root in the northeast US) because it helps the lowest-scoring people the best. Also, one of my teachers did a linear scale thst wasn't constant: multiply by 2/3 and add 34 (y = 2x/3 + 34), which I also liked because it helps the lower scores more, but isn't as extreme as the Texas Square Root. Under the 2/3 linear method, the grade brackets are as follows: A: 84-100 B: 69-83 C: 54-68 D: 39-53 F:

[@hamzacokic2314]

Youre amazing for doing mathematical stuff just for fun. I like maths more now because of you.

[@SolomonUcko]

What one of my teachers did and makes a lot of sense to me is to remove any questions more than half the class got wrong from the total possible points.

[@marshallc6215]

10*root(x) is the best curve for high difficulty classes (like differential equations) because alongside maintaining the 0-100 scale and not decreasing anyone's score, a 50% becomes passing, and knowing half the things *perfectly* is good enough. College is setting the foundational knowledge for you to learn how the world works on the job and isn't supposed to be all you learn. It also benefits the average student the most, as those who are pushing for As post-curve (90%) will still have to push for 81% pre-curve, which is really difficult in some specializations. It's also bad to grade students against each other, because it incentivizes the students to either game the rules of the system (e.g. all students in system 3 skip the test then everyone gets curved to 100) or to intentionally not push themselves academically so that they can get really high grades in really easy courses, rather than doing harder courses in order to learn more. Degrees are not a scarce resource, so saying you knew 90% of the material but everyone else in the class knew 91% of the material therefore you fail makes zero sense.

[@marshallc6215]

@@username8644 you clearly haven't taken any high level technical courses like i was talking about, because a reliable 80% is uncommon. Most students will study their ass off and still only get 50%.

[@marshallc6215]

@@username8644 you've actually argued against your own point. If I bust my butt studying to change what would have been an 85 to a 95, but everybody gets a flat 15% "curve," then I literally wasted my time studying to learn more, which should absolutely never happen. If I got an 85% + 15, then I effectively got a 17% score boost up to 100, but if I got a 60% + 15, I got a 25% score boost up to 75%. It's kind of silly to say that a flat score boost is the "most equal" way to boost scores because you're choosing a metric that reflects the boost being equal for everyone. I don't care about equality. I care about equity. The whole point of a square root curve is that it's viable to make an insanely hard exam such that 50% is the goal, and it also allows nickle and diming small mistakes without failing due to them.

[@deidara_8598]

Not only data scientist; cryptographer and AI researcher are also well-paying profession for those of us with a love for math. A lot of mathematics is also traferrable to computer science, which also opens up a lot of doors for good jobs.

[@cubicinfinity2]

As a data scientist, I can tell you that the data on the salaries has a lot of missing values and doesn't represent the lower range of data scientists.

[@cybersharq427]

Wow cool perspective of what happens behind the test scores that magically appear. Also video on standard deviation would be amazing.

[@graysonking16]

My favorite method utilized in a physics class I took at MIT was to construct a histogram with everyone's scores, then try to make grade boundaries follow the natural boundaries of the dataset. Eg) 100,91,90,88,80,78,75,56,50,32,15 would probably result in one A, three Bs, 3 Cs, 2 D's and 2 F's. Obviously, he tried to give benefit of the doubt, but this did a good job incentivizing students to keep up with their peers, but it didn't prevent collaboration. If the student who scored 100 can get 3 other students to score 100 as well, it doesn't hurt her at all.

[@maitland1007]

In my mind, the main reason for a curve isn't to "give extra credit" but to normalize to counter the effects of things like tests that were too hard, etc. The normal distribution method does that, but here you arbitrarily chose units of 1SD as the cutoff points. This means you'd need to be in the 5th percentile to get an A, as you well know. Why not chose cutoff points such that an A would be the 10th percentile, a B the 20th, etc? Your examples seemed deliberately chosen to be bad ideas.

[@amitshoval7653]

Nice video, I would like to see you do more videos about statistics!

[@Baughbe]

In high school our physics teacher did some sort of curving on the grades that was as he explained to bring the average student to a C grade. But he was also using the Harvard College Physics book to teach the high school class (don't knock it, the Navy got a lot of nuclear specialists from our school). However, it had a really interesting effect for those who actually did well on the tests... with one student on one test walking out with a score of 141.

[@forgetittube5882]

You left out one variation of the “normal curve” :: adjusted mean/standard deviation. You fix the “desired/target” mean/standard deviation (Mdesired/Sdesired) and “adjust” all scores properly. Xnew == (Xreal - Mreal) * (Sdesired/Sreal) + Mdesired. And grade them “as usual” using Xnew scores (instead of Xreal)

[@nickdigrispino2409]

I'm reminded of my high school American History teacher (he had a Ph.D), who said on the subject of curving, " a C is never an A." I teach high school geometry and I'll have to really look into these methods. Thanks!

[@ThomasTheThermonuclearBomb]

For the normal curve (#3), I really don’t understand it. One guy got a 96 on the exam, but he only got a B just because everyone else failed. He should get even more credit because he did better on an exam that most people didn’t. I know blackpenredpen is just showing it, but I am curious why it’s considered the “normal” curve to reward people who did bad and punish people who did good *because* of the people who did bad

[@hashclash6596]

There’s no law that “A” has to be 2 SD from the mean, and it’s kinda odd that he set it that way in the video. A better thing would be to choose a percentile to get A’s like he did in the last example or a smaller multiple of the SD. Only 5% get A’s at 2 SD, whereas he says 20% makes sense in the last example.

[@TheSourovAqib]

I like multiplying by 0 then adding 100😃

[@holdencovington151]

Where I’m from, that third method is called a forced curve. I went to school at Auburn, and we didn’t do that, which I think helped foster collaboration. When you classmates aren’t your competition, helping someone else doesn’t hurt your chances of success! The other side of that was that Auburn is NOTORIOUS for grade deflation. Once I got into my engineering courses, I don’t think k ever saw a class average above 70%.

[@shrankai7285]

I prefer the first method. Though I am not sure about the idea of curving in the first place

[@rorydaulton6858]

My method basically removes a fraction of the student's mistakes then adds a certain value. In particular, I do an affine transformation of the grades [i.e. f(x) = ax + b for some constants a and b] and choose the constants so the standard deviation of the results is 1.5 times the distance between letter grades (1.5*10 = 15 with your grade scale) and the mean is in the middle of the C range (74.5 with your grade scale). So in your given example I would use the transformation f(x) = 0.73*x + 31. That results in the distribution A=2, B=1, C=4, D=1, F=2. I do this in such a way that I ensure that no grade goes down. Of course, this is all done in a spreadsheet.

[@sweetcornwhiskey]

I think the best way to do it is a modified form of the square root * 10 function. Take the scores x in [0,1] (by dividing, by 100). Then, if, say 0.85 is the center of the B range, and m is the mean of the scores, solve m^y = 0.85 for y to get the power to which the scores will be taken. Then, take x^y for all x, multiply by 100, and you have the scores, scaled such that the center of the scores is in the center of the B range.

[@lul_9629]

看到你在How哥的影片留言剛好就來了而且我讀資工的超需要看這些

[@sebalo689]

I love the 10*sqrtX because it preserves ranking and doesn’t penalize anyone

[@lazergurka-smerlin6561]

The third grading curve reminds me of the old grading system swedish schools used to use. Namely they distributed the grades according to a curve which made it so that only your relative skill mattered. Thus the best way to get a high score was to be in a overall bad class, not great

[@doublej1076]

I mostly had two curves used on classes in high school or college. The simpler one multiplied all the scores by (100 / highestScore) so everybody's grade went up, but it helped the kids up top more since the multiplier benefits people who already had a higher score. The second used a bell curve where X people got As and Fs, Y people got Bs and Ds, and Z people got Cs. Anyone whose score would have gotten them a grade "naturally" wouldn't go down, but if a group didn't have enough people the next group down would move up. I don't think moved people counted as extra spaces, so if A needed one person and B needed 3, one B would move up but still only 3 Cs would move, not four.

[@SomethingUnoriginalandDumb]

I’m my stats class we have learned that the way to get a small standard deviation would be to have a bigger n. Your n of 10 seems really small. I think that class changes vary a lot however, in my opinion, I think class sizes are generally bigger like 25-35 for high school students. I understand that you use a smaller n for simplicity but I think that the normal curve isn’t represented to it potential. I don’t think it’s the best but I don’t think it was shown to it’s full potential. Thank you for the video! I learned a lot! :)

[@mariag2916]

I love you - you are amazing! Thank you very much for your videos!

[@blackpenredpen]

Thank you l! 😃

[@adrien5568]

What some of my teachers used to do was : Take the max and the min, says they're equivalent to 100 and 50. Then linearly transforms the others. Everybody gets a passable note, and the ranking is globally the same.

[@stephenbeck7222]

This is the Kennedy scale I referenced in an earlier comment.

[@blackpenredpen]

How would that be with the example in this video?

[@adrien5568]

​@@stephenbeck7222 I looked at the Kennedy scale and I don't see how it's the same? Unless I missed or misunderstood something important. In this method, you don't care about the mean, just the lowest and highest scores. The formula is simple. Let S be the scores, m = min(S), M = max(S) and f(x) the function that maps S to C the curved scores. f(x)=50+50.(x-m)/(M-m). The scores in the video will then be (rounded to the nearest integer) : 50, 53, 59, 71, 72, 74, 76, 86, 89, 100.

[@adrien5568]

@@blackpenredpen see above

[@adrien5568]

I may have to add that I'm french and our education system is sometimes a bit weird (also our grades are from 0 to 20).

[@hgh468]

Curving scores is just like doing image processing. So we can use as many ways as we can to enhance the "pixel brightness". e.g., a histogram equalization can also be used.

[@eris4734]

My teachers sometimes used a 'floor', so the range of scores instead of being 0-100, they'd become something like 50-100, so they'd do something like divide the score in half and add fifty, or for a floor of n, s' = s*(100-n)/100+n = s+n-sn/100

[@MagnusSkiptonLLC]

I remember my high school biology class. I think I was getting a 78% in the class, and I got an 85% on the final...and it ended up making my grade go down. I talked to the teacher and apparently he averaged tests, homework, etc. in their own buckets, then averaged those buckets together, and my test bucket had been higher than 85% before the final. So it made that bucket go down, and thus my whole grade go down. Then he yelled at me because apparently he had explained all this at the beginning of the school year, like 9 months prior, and explicitly didn't want us asking him why if this happened. Yeah, he was an ass.

[@robertveith6383]

hole.

[@hogo21]

Rip

[@yankeery12]

What that tells me is that you put in a significantly small amount of effort into labs and homework lol. Especially since your test average was above 85 and you ended up getting a final grade below 78 lol how many late assignments did you turn in bruh

[@RandyKing314]

first, thank you for explicitly stating that “curving” is simply granting extra credit! next, if an instructor does grant this credit with a grade adjustment, i like the process of compacting the distribution upward by calculating ratios based on an adjusted fail point. this preserves the distribution exactly (important to me as a measure of fairness). not “curving,” but adjusting

[@christianstonecipher1547]

I mean when half the methods have the potential to harm a student's grade I would argue that curving is not simply granting extra credit. It would be more apt to say that curving is the teacher manipulating the grade in such a way as to where the final scores would more closely conform to what the teacher wants the distribution to be. Sure that can come in the form of granting extra credit like the first 2 examples but the last 2 examples were definitely not simply granting extra credit, it was adjust scores so that they fit what the teacher decided was the proper distribution for the test results. Both the last 2 have the possibility for a score of 90 or higher being graded as an f which is definitely not granting extra credit. (While many teachers will make sure that curves will not hurt somebodies grade that is not guaranteed)

[@SweatyFujoshi]

a very long time ago when i was in school, the curving method that was used was essentially a proportion method. whoever got the highest score got it multiplied by some number to make their score 100, and then everyone else got multiplied by the same number. in your example it would be pretty minimal because one person got 96 (not to mention someone getting 100 "breaks" the curve) but it does get a lot better if no one did well at all.

[@BlackSoap361]

In high school, one teacher used square root * 10 for tests. Also, sometimes bonus questions that were worth 1 point each, but only if you already got all the main questions. In college, some courses the professor figured out what would make the 3rd highest score an A, and increased everyone’s scores proportionally. If he based the curve on the top two scores, nobody else would pass.

[@renderize69]

*The first one is mind blowing, wish my country uses it*

[@devinturner4236]

My Calc 2/3 professor was the only professor I've ever had that curved, and I'm not really sure what his exact process was. Questions were all worth a certain amount of points but he would normally have the test out of less than what they all added to, not sure if he was just using the highest score achieved as what it was out of or if he just chose in advance to give us leeway but it worked out well enough for me.

[@arekwittbrodt]

One of my teachers used method nr 3. It worked perfectly, because the mean was always around 30 :-D

[@shawnheidingsfelder8179]

In my experience, we got points added if there was something like an unfair question (no one got it right, or it was confusing), or if there was something on the test that wasn't covered in class but snuck on the test anyway (teacher just used prewritten tests from the book and forgot we didn't cover something). Otherwise, if there was a curve, usually the highest grade became 100%, and everyone else just got a letter grade based on that, so if for example the best grade was a 92 out of 100, then 92 became the most points you could get, and the scale was made off of 92, not 100. I've also had classes in college where the highest grade earners were graded differently than the rest of the class. My German language class was like this, because several people in it were native German speakers, and it wasn't fair to the rest of us to grade our efforts based on what they were doing. The teacher held them to a higher standard.

[@in-ty8vb]

I am actually learning about the normal distribution in school. Our math classes contain a lot of statistics and working with probabilities. And yes, I know how to find the standard deviation without a computer

[@dudono1744]

if i remember well it's the quadratic average of difference between each data and average. might have used wrong words since english isn't my main language

[@nandeesh2ninad]

Sir can you please show us an easy way to identify the conic by looking at the general 2nd degree equation please🙏🏻🙏🏻

[@an_eternal_kaitakusha]

I know some teachers will compare the students original grading and the grading after taking the third method, and see which one is higher. I think this is the best way.

[@axoluna]

My Calc 1 teacher curves her final like this: it was out of 210 at first, but then her 10th best score (of ~50 kids) was the max. So say #10 got 203, then if your score was 176 your curved score is 176/203 as a percentage. In this example If you scored higher than 203 you get more than 100%.

[@abdullahimohamedalasow7783]

nice video. thanks

[@Stormorbiter]

First way is the best though sqrt is arbitrary. To generalize, you can use any root you want. Instead of 10*x^(1/2) do (100^(r-1)*x)^(1/r) for any r>=1

[@mikeholt2112]

I haven’t seen this comment, so I’ll chime in: I think the width of each bucket for the normal curve should be 1 SD whereas you have the C’s at 2. This changes the Z scores to -1.5 for F, -0.5 for D, -0.5 to +0.5 for C, then B, then +1.5 for A.

[@dfp_01]

I'm pretty sure my high school physics teacher would calculate the Z-scores of our test grades and generate our curved scores using some normal distribution, like with a mean of 75 and a SD of 10 or something. I'm not sure exactly

[@harryfazekas4238]

In my universty was log2 curve: 50%>E, 50-74:D,75-87:C,88-93:B,94

[@prosaicGodowsky]

Commenting to ask this man to teach us to compute standard deviation by hand

[@givrally7634]

My guess as to how they found that formula is that they didn't see scores as going from 0 to 100, but from 0 to 1. In that way, you just need a function that has the following properties : 1) f takes [0,1] to [0,1] continuously 2) f(0)=0 and f(1)=1 3) f(x)>x for x between 0 and 1 excluded The square root function is one good way to do it, as is x^p for p between 0 and 1, and min(x+0.15,1) if you don't mind the zero grade becoming a 15. If you want to go back to the original, just know that the real score is 100 times that, and the score you use in the calculation is the score divided by 100. So the real score becomes 100f(x/100), which comes out to 10√x or min(x+15,100). The other two methods don't actually follow those rules since the score you get can actually be lower than the one you were supposed to (if, say, you get 98 and everyone else gets 99, you'll end up with a D or even an F)

[@lidarman2]

I just noticed all the markers on that shelf. :-O .That's hilarious. Never noticed that before.

[@ALeafOnTheWind42]

When I need to curve, it's because the mean is lower than I want it to be. I will then add an amount of points to everyone's score to force the mean to that value

[@Tridip_SSC]

Love from India 💖 Thanks its super helpful🙏

[@muhilan8540]

They used the square-root curve in my high school in the US too

[@GRBtutorials]

Related to this, is how you combine exam score with classwork score. It can be as simple as a weighted mean (example: exam counts 80%, classwork 20%), and in at least in my uni it usually is, but there are more convoluted possibilities. For example, I had a class where the score (from 0 to 10 as it's customary here) was calculated as E + 0.2C [1 - (E/10)^3], where E is the exam score and C is the classwork score. This function has the interesting property that it always gives a score greater than or equal to the exam score (as long as it's from 0 to 10, which is always the case).

[@dudono1744]

use harmonic mean (aka 2 / (1/E + 1/C) ) to stomp people who rush exams (or cheaters) or lay down on exams

[@19TonsOfGold]

This is kind of similar to the 10*sqrt(x) method but was based on my observation that effort that goes towards 100% leads to diminishing returns analogous to diminishing returns from accelerating to the speed of light due to relativistic effects. Thus, the method is y = tanh(invtanh(x)+b), where b increases scores if positive and decreases if negative. For example, if b is 0.1: 0 becomes 9.9% 42.5% becomes 50.3%, just barely passed 75% becomes 79% 95% becomes 95.9% Likewise, if b is -0.1: 10% becomes a 0 (and lower scores would clip to 0) 50% becomes 42.1% and thus fails 75% becomes 70.2% 95% becomes 93.9% Multiplying by b instead of adding leads to a bigger boost for the middle rather than the bottom, but works the same as 10*sqrt(x). However, whatever method would be used, the actual decision to use it would be contextual based on the circumstances of the year, and the effects on how it would motivate students. At the least, I think it should be *possible* for every student to pass (even if there's almost always some who don't). Also since the most common scores people would be concerned about changing is from fail to pass followed by a B to A or D to HD, these would be the cases that would warrant review, but only if the student missed the mark by 1% or less. As far as I remember from university, these adjustments would only happen if the student was known to put in the effort through attendance and completing all the assignments.

[@davidhuang2895]

One curve my professor implemented is pretty smart because it rewarded the students who did better. This example assumes that the student scored X, with the curve being A. Rather than method 2, in which students would get their score as X+A, my professor would curve so that the grade is X(1+A).

[@mirzaghalibkiyaad325]

I'm from India and I like your contant Your video is very helpfull sir

[@thecreator3528]

@blackpenredpen could you make a video about the derivation of the Taylor Series in Multiple Dimensions. I'm studying physics and came across this hunge monster of an approximation, but I can't seem to derive it after trying for a long period of time. I noticed that there isn't much to find about the derivation of the Taylor Series in Multiple Dimensions, so I thougt you could make a video about it. Thanks in advance!

[@lior_shiboli]

at an especially low score test we got 1.2X+6 curve which is like +15 points or more(since if you get less than 45 you are not passing anyway and have to take the course again) i assume that was in order to further help students who were particularly good get more points or something

[@DangRenBo]

Method #5 -- I sometimes do a linear transformation to raise the top score to 100 and the average to an average that makes sense. Method #6: I have also used the method mentioned by Michael in another comment where I map the mean / SD onto a new mean / new SD.

[@8543960]

I seem to remember the most common method at the college I attended among professors who curved was to scale every grade relative to the highest in the class. So if the highest on an exam was, say 84, that grade would be 100 or an A. A score of 60 would become 71 (60/84*100) or a C. I would note these profs would give extraordinarily difficult exams with at least one question virtually no one would be able to answer correctly and there was rarely anyone who could break the curve and actually get a raw score of 100.

[@craighalpin896]

I had the same but there was one exam where I made a perfect score and even managed some extra credit... I got 105%. Most of The rest of the class got scores in 70% range.. the professor asked if the class wanted him to curve the exam. The class all agreed and the professor laughed when he realized the top score and gave a small cautionary tail that they should not blindly jump to wanting to curve the test without knowing the top score. He told them that it would leave them all with a lower score.. but agreed to curve the test based on the 2nd highest score that was in the 80% range leaving my score unchanged. I enjoyed that class😆

[@jawahirkhan568]

Of course you did.

[@DGol2015]

One property of the square root curve I've noticed is that generally, lower scores gain more of a boost than higher scores. This is nice because the main reason to curve is to save the low-scoring students' grades. But there's an issue with that property not working below 25% (actually might be 15). I used it once or twice and had to make that part of the curve the minimum score. There are probably some horizontal transformations i could do to improve it, but it was kind of a headache. I wish these kids would just score higher. 😣

[@elchingon12346]

For the normal curve, if you want to be nice you can move each letter grade back one standard deviation, so a B is within one standard deviation

[@blackpenredpen]

Yea, it will be so much nicer!

[@maxb.1302]

My professors always used the tactic of setting the passing grade (starts at 50%) to the highest number of points below 50% where at least half of the class passes. The grades get adjusted accordingly while only the A just gets a larger range.

[@driveral1305]

The curve grading format I was always used to had the top score on a test, or course as a whole, as the 100% benchmark if no one scored 100%. The grades used the standard percentages from the highest score >90%=A, >80%=B, etc... So if the highest grade was a 90%, anything above 81% was an A. 72% or above was a B, etc...it wasn't used for more fairness in the class, it was used more to measure the difficulty of an exam or course. Generally speaking, there were very few 100% exams and fewer still in a full course.

[@dfp_01]

My favorite simple method is where you set the mean of the curved scores (e.g. 75%) and add to everyone's initial scores the difference between their mean and your target mean. So this group that had 59.3% average would get 15.7 extra points-not far from just simply adding 15

[@stephenhousman6975]

I can't remember how my HS calculus teacher did it but he did a grading curve similar to how the AP tests score because his test were designed similar to the AP tests.

[@sevret313]

I think the "system" that is used in unis here in Norway is that with time the passing exam grades should follow a normal-ish distrubution but no single exams is adjusted unless something seriously wrong happened like half the class failed. Instead the difficulty of the exams need to be honed in so you get a reasonable distrubution.

[@MrRogordo]

That's what we do here in Colombia. We expect a normal distribution so the average student will pass with a little extra over the treshold. Because we don't use letter grading systems, our credits are our final grades. So, if a disaster (like you claimed, 50% failing an exam) happens, what we usually do is take the mean of the grades the students got, and "displace" everyone's score so the new mean is the required passing score. This gives a flat boost to everyone while preserving the real distribution

[@christinagraceduallo7731]

I just wish to have those kinds of professors who'll help their students pass.

[@amirhosseinmaghsoodi388]

The method one of my teachers used was to set the second best score as 20(our grades go from 0 to 20) and scale the rest accordingly.

[@kumeboyahh4843]

I’m currently in AP Calc AB as a junior and I never learned how to calculate standard dev by hand could you do a video on it?

[@markkaz7754]

My teachers did a linear regression curve for my calc class

[@jasperquartz3726]

the most helpful way i've had teachers curve grades is to have students do corrections and then grade the corrections. Students get the graded test back, correct the questions they got wrong (open book, showing work, can ask professor questions in office hours), the professor or grader grades the corrections the same as the test (ie, questions that the student got right are still right and the grader doesn't need to look at them, while questions that the student got wrong and has fixed in a way that demonstrates the student has learned since taking the test become correct). Then the final grade is the arithmetic mean of the original test grade and the corrections grade. so a student who got 100 on the test would not need to do corrections, while a student who got 32 on the test could have a final grade of up to (100+32)/2=66 if they worked very hard on the corrections and learned the material after the test, but would not get extra credit if they don't do the corrections. I had a high school geometry teacher and a introductory college chemistry professor who did this. If the goal is for students to learn the material and be prepared for the next unit or the next course, test corrections that are worth lots of extra credit gives students who did badly a reason not to give up on the class and a structured way to study the parts of the subject that they don't understand, meanwhile students who did well will just be happy that they don't have much homework Mathematically if x is the original grade, then the final grade is between x and (100+x)/2 inclusive

[@MusicalPlatypus101]

I had a Physics professor who did the “normal curve” method but curved to ALL the students he had over his 15+ years of teaching, so it was fair from year to year.

[@brentkreinop1716]

As a senior in high school, I took AP calculus with all the rest of the honor students. I did exactly one homework assignment all year, because it was the only one collected for a grade. I missed less than ten exam questions all year, but there were enough other at my level to make curving the results unnecessary. When my next younger brother walked into AP calculus on his first day, dressed in overalls, flannel shirt and cowboy boots, everyone else in the room assumed he was in the wrong room. A number of them, when recieving their results from the first exam, asked for the teacher to curve the scores, were shocked to find that the teacher had done the prep work on that and found that my brother's score was so much higher than theirs that he would break the curve in such a way that the ones who asked would have actually gotten lower grades with the curve than without.

[@amstereo8402]

My differential equations professor sent me to your channel

[@dudono1744]

students: could you curve? teacher: *curves in a way that lowers scores* students: you weren't supposed to do that

[@blackpenredpen]

Let's differentiate their scores! : )

[@dudono1744]

isn't differentitation similar to derivation? wouldn't make sense on discrete values

[@OrdinarySonicfanMmKay]

Standard deviation: sqrt((sum(x_i-mean)^2/total) NOTE: Some graphing calculator apps (like Desmos) have statistic functions built in

[@Akhulud]

I think that 10sqrt(x) = sqrt(100x) which is the geometric average, which is bigger or equal to min(100,x) and less or equal to max(100,x)

[@sashimanu]

The only valid curve is linear y = 1x + 0

[@elchingon12346]

I’m so glad you talked about the square root curve! I’ve been using that for the last two years and no one has heard about it, even in the math department 😂 Edit: I only work with decimals on the grade book side of things, so since everything is a decimal already my curve function is just sq.rt(x), I don’t need to multiply by 10

[@blackpenredpen]

Yea! In fact, a friend's mom told me about this in her college days and that's how I learned about it (I didn't attend colleges in Taiwan). And I was so fascinated by this method and it led to this video! : ) Btw, how did you know about the 10sqrt(x) method?

[@elchingon12346]

@@blackpenredpen in my first year of teaching I didn’t know about any tried and true curving methods, so when I looked online I saw a whole lot of curving methods, but this is the only one that used a function. I wanted something that could be automated and I thought “how clever, sqrt(x)>x for all values between 0 and 1!”

[@misteroking]

My professors use a different kind of the normal way. They take the mean and if it's lover than C they add the difference to everybody's grades so it pushes the mean to C. Then, they use the normal scores as A=90-100, B=80-90 and such to grade. It kinda does the same thing with the normal way but rather than changing the grade borders they push the mean up to C. I like their method better.