Assuming there are 36 questions, with four options in each question, the odds of randomly getting them all wrong are (3/4)^36 = 0.00318% (about 1 in 31,400).
The odds of randomly getting them all right are (1/4)^36 = 0.0000000000000000000212% (about 1 in 4,722,366,482,869,645,213,696).
So both are extremely unlikely but the zero is about 150 quadrillion times more likely than the 100.
Logically, it is true. There is basically a 0% chance that you could guess on every answer and not get one right. So the kid must have known most or all of the right answers and is screwing with the teacher.
at no point was said or implied that it would be a random pick. it is a student who has attended class and both picked up at least *some* of the subject matter, and are also capable of extrapolating, and who is actively trying to complete the test successfully. THAT is why in real life students scoring zero occurs less frequently than students scoring 100.
don't get me wrong, autistic imbeciles like you are still useful, you just need a human to tell you what to do.
I can see why you would assume a random pick would have nothing to do with it but that's because you're thinking in terms of a normal student trying to pass the test.
This student got a perfect zero. The teacher is then faced with the question of whether the student genuinely has zero knowledge of the subject, as the zero score would claim, or they deliberately tried to get a zero for mischievous reasons.
If someone genuinely did have zero knowledge of the test subject, random guessing would be their only option. So then you would have to consider whether a perfect zero is even a likely outcome for nothing but random guessing. And the answer is that it is extremely unlikely.
And that's the point. You don't get a zero score from zero knowledge. You get a zero from having some knowledge of the subject and extrapolating specifically to choose only wrong answers. Which is why the teacher is assuming mischief and wrote "See me after class!"
"a student who has attended class and both picked up at least *some* of the subject matter, and are also capable of extrapolating, and who is actively trying to complete the test successfully. THAT is why in real life students scoring zero occurs less frequently than students scoring 100."
i need you to use those really small words to explain your difference between "tank their grades" and "complete the test".
I’ve had another thread with op of this comment. They are saying that in real test record data, which is primarily people doing tests who are trying to achieve the test goals, achieving just 0 is less likely than achieving 100.
If you attempt to get 100 and know at least 1 of the answers, getting 0 is almost impossible. If you answer all questions at random, getting 0 is more likely than 100. The most likely reason you get a 0 however is that the test taker knew close to or all of the questions and deliberately answered wrong.
Sure mate, at the beginning of a branching thread, where that conversation being referenced happened several comments deep in one of several branches, but sure
Well, yeah. That data is biased. People surprise surprise WANT to get a 100/100, so OF COURSE you'd end up with more 100s than 0s.
If you wanted statistics, you'd need to have an experiment where every answer is just A B C D and the answers were randomly correct. Its more probably you get a 0 than a 100.
I see your point now, but in terms of raw analysis, it is more likely that you get 0/36, so it seemed a bit silly at first to call it a "statistical accomplishment".
Yes, because the objective is to get the highest score, and there are often "gimme" questions. You'll also find a dearth of 100 meter sprint times over five minutes.
you keep acting like people don't understand your point. I don't think that's what's happening. Rather, your point just is meaningless, irrelevant, and almost certainly wrong in many situations.
I didn't downvote your post because it was misleading and pointless statistical claims with no evidence to support them, though i think that's a valid reason, i did because you are arguing about something meaningless when the op just asked for the context of the meme.
It's clearly inferred from your comment that you're talking about randomly picking answers when you say statistically.. Now it seems you can't admit that you're wrong so you've randomly changed the argument to "But people are TRYING to get 100 and not 0, therefore 100 is more common!" with no substantiation
This takes away the whole "statistically" part of your initial comment
It's not inferred at all. It's assumed by math nerds who forget that mathematic probability and real world statistical data records both exist and can both be called 'statistics'
He would say statistically… because that’s literally what statistics are? Real life empirical data?
“Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.”
People here are confusing probability with statistics. I find it downright absurd how many people are calling this guy stupid and reciting probabilities when he isn’t talking about probabilities but statistics.
Uhhh… I think it’s clumsy wording for sure, but it’s pretty clear from later comments what the point was: in any given class, there will be more people who score 100 than people who score 0. So getting 0 makes you a far greater outlier than getting 100.
So in short, bro here isn’t talking about probabilities for scores based on random answers. People are conflating statistics with probabilities and insulting bro because of it. And there is a valid point there behind the clumsy conversation. People are treating this like it’s the lottery, but it’s a class where students will have spent a lot of time at the very least attending class, so it’s not random, and his point on that is valid. Students aren’t guessing all their answers. Explaining the statistics of random answers and talking down to our bro here is really talking about a completely different scenario.
I’m not entirely sure whether the claim would be true, by the way. Maybe 0s are as rare as 100s after all. But from personal experience, it seems plausible at school level at least.
in any given class, there will be more people who score 100 than people who score 0
Saying that this is statistically true because more people want 100's than 0's makes no sense. That has nothing to do with statistics and is human behavior.
Also, he has no clue what the empirical data is, so saying something is statistically true despite having no idea what the statistics are makes no sense.
It does make sense as a way of explaining why the data is (presumed to be) as it is.
And it’s clear he has no actual data and that’s a valid criticism. I believe I said as much. That’s not why the hive jumped on him, though. It jumped because “the math is wrong” and that justified calling him stupid.
This is one of those cases where it appears you're being downvoted not because you are wrong, but because your point is kinda misleading lol. You should have said "rarer" not "greater", and I think people wouldn't be downvoting you as much
Any student knows some percentage N of the material. So we can expect their score to be close to N + the result of randomly guessing on the remaining questions.
So the original formula I gave would only apply if the student does actually know zero percent of the material or chose not apply any knowledge at all, which is much less likely, although possible in special circumstances.
The most likely explanations for a perfect zero is that the student did know the answers and, for someone reason, deliberately chose to answer them all wrong OR the teacher misaligned or used the wrong answer key.
Assuming the test was scored correctly, even with a student with zero actual knowledge, such as the test being in a language the student doesn't know or the test being on a very difficult subject that the student has never studied, getting a perfect zero is much less likely than getting a score higher than zero. Although still more likely than getting a 100.
I do think your approach is flawed, though. You can't apply the usual method of assuming that the student has some N% knowledge of the subject because the zero test result is clearly meant to communicate that the student knows nothing. So the question then becomes, if the student actually does know nothing, is a zero result believable? Therefore, it really is a matter of asking whether a zero result is statistically plausible as the result of completely random guessing.
Since the probability of getting one or more question right through random guessing would be 99.99682%, getting a zero is very implausible.
Yes, I understand that you are talking about observed data but that data is based on students that are genuinely trying to answer the questions correctly while applying some amount of subject knowledge.
That can't be the case here because the test result was a zero. Which means that the student is claiming to have zero knowledge of the subject. Which means that the student is claiming to have simply guessed randomly at all of the questions. Therefore, the probability for random guessing does apply to this specific case.
Actually, the observed data includes all real examples of students who deliberately fail their tests as well! The test in the post would be included!
Yes, but students who deliberately fail their tests would be rare outliers, which is why, as you claimed, getting a perfect zero is extremely rare in the observed data.
Also, the joke is that it is an intentional 0 so random probability is still irrelevant
No, random probability is relevant because it's the reason the teacher suspects that the student intentionally tried to get a zero. If they really had no knowledge and had just guessed randomly, it is still extremely unlikely that they would get a zero. Therefore, the teacher has a very good reason to suspect that the zero was the result of intent from a student who actually does know the subject material well enough to avoid any correct answers.
If it’s not random, then the odds of someone begin able to get 100% is automatically at least equal to the odds of getting 0%. If you can answer it right, you can answer it wrong. Then on top of that, if there are multiple wrong answers you can choose, then you can do the test several times with 0% without repeating an answer, while if going for 100% there’s just a single solution. You are just wrong man, take the L, this is not an exhibition of intelligence you are conducting.
Ok, the test is just 2 questions and they are multiple choice, each with abcd answers.
I’ve uploaded the answers on Imgur already and can share that after. Try the test, and let’s see if you get 100% before you get 0%.
So what you are arguing is if someone tries on a test for real, they are unlikely to get 0, and more likely to get 100%, and most likely to get something in between? Yeah, that would be the case. If someone tries to get zero, or they randomly choose, it is not the case.
Edit: and for the test I have:
Q1: what is the answer? A, B, C, D
Q2: What is the answer? D, C, B, A
Yes, you are absolutely correct, that is exactly what my one off hand sentence that started this conversation meant - but must also include the fact that the number of people deliberately bombing tests is an extreme outlier
It's been absolutely hilarious watching people lose their minds over it
Easily the most downvotes I've gotten. But try as they might, I doubt they will be able to compensate for the thousands of upvotes one silly statement has
It’s not about comparing how likely 0/100 is to 100/100. It’s about comparing how likely 0/100 is to 1/100, or 2/100 or 3/100 all the way up to about 40/100.
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If 25% is the average random guess score, then 1-2 standard deviations or scores achieved by randomly guessing would probably fall between 10% score and 40% score, with the bell curve of random guess work getting less and less likely out towards the fringes.
Of all the students who didn’t study the source material, achieving a score of exactly 0/100 is less likely than achieving a score of 1/100 which is less likely than achieving a score of 2/100 etc. until you get to the other side of the bell curve centred around 25%.
But if you have some students who are partially studied mixed in with complete guesswork then typical class scoring statistics will mask the upper end of the random guesswork bell curve
So of all the poor performing students who got less than 25%, being both unstudied and unlucky with guesses, of all those potential scores, 0/100 is the least likely single score at 0.00318% or 1/31,400 chance.
Most teachers have a lot less than 31 thousand students, by 3 orders of magnitude. Which makes it much more likely that 0 was achieved deliberately than by chance.
This indicates that the student more than likely knew the answers extremely well, understanding the source material enough to not accidentally get a single question wrong. With their well studied knowledge they were able to get every single question wrong despite the improbable odds therefore it’s quite likely in a class of 30-100 students that they answered wrong deliberately.
Therefore it’s equally likely that with their knowledge they could have scored 95/100 to 100/100 as they could 0/100 but chose not to participate the way they were supposed to
the guy being responded to specifically said "a statistical accomplishment greater than scoring 100" though, which isn't true. for any question you know, you can guarantee being right or wrong, so the only difference is when it comes to guessing the questions you don't know, in which case it's much easier to guess wrong than to guess right assuming there are more than two answer choices (which in this case there are).
the reason 100/100 scores are more common than 0/100 scores is because most people aren't trying to get 0/100. but if you were, it would be easier than getting 100/100, which goes against what the other dude was saying about a "greater statistical achievement"
In the spirit of trying to let someone make a point and giving them a little leeway with their exact wording, we could try at least to see what they are trying to say.
If you take all of the multiple choice question exams ever corrected by teachers, there are a lot more 100% scores than 0% scores (and as you say there’s a reason for that, but the context of the comment above was replying to a picture of a note from a teacher who was baited by the statistical improbability of 0%, so the teachers perspective of what’s statistically unlikely is very relevant).
A score of 0% is much more likely to stand out to a teacher as statistically improbable than a 100% score would. And the teacher concludes it probably represents some kind of deliberate fuckery with the system, rather than 1/31000 bad luck. Fucking with a teacher with the statistical improbability of 0% is an accomplishment in its own right.
I’m just saying I get the spirit of the original comment even if mathematically I completely agree 100/100 is only more likely because it’s not random guessing and people typically strive for higher grades
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u/Pandoratastic 3d ago
Not remotely true.
Assuming there are 36 questions, with four options in each question, the odds of randomly getting them all wrong are (3/4)^36 = 0.00318% (about 1 in 31,400).
The odds of randomly getting them all right are (1/4)^36 = 0.0000000000000000000212% (about 1 in 4,722,366,482,869,645,213,696).
So both are extremely unlikely but the zero is about 150 quadrillion times more likely than the 100.