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deathtocapslock2021-02-07 07:33 pm
sunnyskywalker) wrote in deathtocapslock2021-02-07 07:33 pm
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How magical are most wizards?
Trying to line up the contradictory statements throughout the series about average magical ability into something coherent is probably a lost cause, but I'll give it a shot anyway.
Based on Harry’s school experiences, it seems like the average witch or wizard ought to be pretty magically powerful. Hogwarts students are expected to turn teapots into tortoises by the end of third year. The OWLs require students to demonstrate spells like making egg cups turn cartwheels, Vanishing iguanas, and banishing Boggarts. And the members of the DA learn what’s supposed to be a very advanced spell, the Patronus Charm, in an evening.
On the other hand, we don’t know how many of those spells students have to perform successfully to get a passing score. Some real-world exams are deliberately set to be so difficult that getting 60% of the questions right is considered pretty good, and 75% about as high as anyone could hope for. (I recall some of the Advanced Placement math and science exams being like this, at least about 20 years ago.) So it’s possible that students can botch quite a few spells on their OWLs and still get decent scores.
With that in mind, here’s Harry’s impression of his Charms practical: "On the whole, Harry thought it went rather well. His Levitation Charm was certainly much better than Malfoy's had been, though he wished he had not mixed up the incantations for Colour Change and Growth Charms, so that the rat he was supposed to be turning orange swelled shockingly and was the size of a badger before Harry could rectify his mistake..."
So, Harry performed one wrong, and a second—which he learned five years ago—was not confirmed as good in any absolute sense but only “better” than Draco’s. We have no idea how this compares to the rest of his practical, but he says of the Defense exam later, "Here, for the first time, Harry felt sure he had passed.” He can’t have performed that many spells successfully on the Charms exam if he wasn’t sure he’d even passed, and yet he earned an Exceeds Expectations. Though maybe he was more worried about the written section. And he did perform that wrong spell successfully, technically. So the issue might be memory, not power.
Still, it makes you wonder whether students aren’t expected to be as capable as the list of exam questions and tasks alone suggests.
Then we get the peculiar claim from Fred and George that a lot of Ministry employees can’t cast a basic Shield Charm. Not that they can’t cast very strong ones, or that they can’t react in time for them to be useful, but that they can’t cast them at all. Many of those employees would be old enough to have taken DADA shortly after the curse kicked in, when it was probably possible to find decent teachers nearly every year; some would be old enough to have studied pre-curse. Even those not much older than Harry could have formed their own study clubs and practiced. And yet that many people can’t perform one of the most basic defensive charms after five to seven years of classes?
We also hear that many people have such “woeful wandwork” that they “find [themselves] making excuses not to perform simple spells,” in the words of Kwikspell’s advertising copy. They may be exaggerating for dramatic effect, but the company exists to make a profit, and they could hardly do that if they didn’t have a large enough market. “Hundreds of witches and wizards have benefitted,” again according to the advertising copy. Within the tiny British wizarding community? Perhaps it’s the worldwide Anglophone community. Or perhaps we ought to revise their claims down a bit and assume the company isn’t as established or successful as they make out. But still.
Worse, lesson one is “Holding Your Wand (Some Useful Tips).” Just how many people within the British or even Anglophone wizarding community don’t even know how to hold a wand properly? One begins to wonder about Lupin’s belief that most British witches and wizards attend Hogwarts. Does he have credible statistics to back that belief?
And then there’s that very odd statement of Neville’s, that even after he magically bounced, his family worried he might not be “magical enough” for Hogwarts. Magical control doesn’t seem to be required for Hogwarts admission, because hardly any students develop anything resembling control over their magic for months after they start, from what we see. Why would think that anyone with enough magical power to bounce after being dropped head-first out the window wouldn’t get a Hogwarts letter? Irrational fear? Or do they know something we don’t? Maybe they know that Filch, or someone else now considered a Squib, performed some comparable magic and yet didn’t get a Hogwarts letter?
Here’s my suspicion: in fact, a large percentage of witches and wizards are magically weak, and many never attend a magical academy. Squibs aren’t as rare as the average wizard believes, either. If you asked every witch and wizard to perform a series of basic spells, many of them just plain couldn’t. Not with any amount of practice or memory-boosting tricks.
What happens is, many families have traditionally put their children through homeschooling and apprenticeships, maybe with some fly-by-night lessons from organizations which are a bit more than tutoring groups but not quite schools. So when a child doesn’t get a Hogwarts letter, or starts Hogwarts but seems too magically weak to succeed (and doesn’t have a family determined to make them succeed, like Neville’s), their family tells everyone that they want their child to learn practical skills instead of silly rats-to-water-goblets spells. Because many magically talented children also do apprenticeships and vocational programs, this isn’t automatically code for “Squib.” People who haven’t observed the child closely might honestly not know whether the kid prefers to learn practical skills or lacks magical power. No one is out gathering data, as far as we know, so even if someone knows a family trying to hide that their children are Squibs, not just working clerical or service jobs which don’t require much magic out of necessity or preference, they might believe—incorrectly—that these are rare exceptions.
The population wouldn’t be neatly split between magically weak people who don’t go to Hogwarts and magically talented people who do, because they can’t always predict aptitude (just look at how wrong everyone got Neville). But the average level of magical power is probably higher among the Hogwarts set, since Squibs don’t get in and magically weak students are probably more likely to leave early than magically strong students.
This leads to an interesting possibility. If people base their expectations of what the average witch or wizard ought to be able to do on a combination of what Hogwarts exams require and what they see people being able to do—or not—they might end up with skewed perceptions. Their conclusions might not be rigorously logical. In fact, they might be downright contradictory, if they actually sat down to work them out step by step, but when have we ever seen the average witch or wizard do that?
So they might think something roughly like this: obviously, the average witch or wizard is powerful, because look at all the hard stuff Hogwarts requires; we know that all that stuff is really hard because look how many people—including those who have never set foot in Hogwarts—can’t do those things. This muddles the abilities of two differently-defined groups: Hogwarts students who pass at least some OWLs versus the entire population.
Things get more interesting if you add historical perspective. Centuries ago, when the wizarding and Muggle worlds weren’t so separate, there would have been more wizard/Muggle marriages, producing children with a range of magical ability. Perhaps until Hogwarts got properly established—or even for a few centuries afterward—they didn’t draw such a sharp distinction between magical and Muggle. Perhaps those who would today be considered Squibs were at one point considered witches and wizards: not powerful enough to handle wands and attend Hogwarts, but witches and wizards all the same.
And what about teaching standards? They aren’t ideal in the Hogwarts we see, but if you look at the history of education, the modern situation improves dramatically by comparison. Medieval and early modern educational institutions were often extremely haphazard affairs. You’d have students roaming from teacher to teacher or even university to university whenever they chose, no set schedule or expectations, frequent riots, students going to school for years without ever quite learning to read… Why should we assume that Hogwarts escaped the social influences that produced these conditions?
Even if we assume it was better than average, a lot of students probably showed up not knowing how to read and with no math skills other than basic counting. Maybe they offered lessons which required little or no reading and writing in the past, or diverted those students into non-Hogwarts vocational programs. But maybe, at least at some points, they took the time to teach basic literacy skills and such. That would leave less time for the kids to practice magic. And if the reading lessons were quick and basic, there might have been a lot of intelligent, talented students who did poorly because they couldn’t get through the required reading or compose acceptable essays. This isn’t exactly uncommon today in more established educational systems; why should Hogwarts centuries ago have done better? It’s possible that even if, like today, the average Hogwarts student of 1300 was more magically powerful than the average witch or wizard from the population as a whole, Hogwarts students in 1300 usually couldn’t perform many more spells than the average hedge witch—as is not true today.
If some spells got a reputation as difficult because most of the magical population couldn’t perform them in 1300, when much of the magical population couldn’t even use wands and many of those who could were poorly trained, this reputation might not hold up when tested against the modern Hogwarts population. That is, it might work like this:
So we find ourselves in an odd position where magic is both harder and easier than wizards generally believe, depending on exactly who is performing it. The magical population as a whole is capable of much less than they think, but most Hogwarts students are capable of more.
Based on Harry’s school experiences, it seems like the average witch or wizard ought to be pretty magically powerful. Hogwarts students are expected to turn teapots into tortoises by the end of third year. The OWLs require students to demonstrate spells like making egg cups turn cartwheels, Vanishing iguanas, and banishing Boggarts. And the members of the DA learn what’s supposed to be a very advanced spell, the Patronus Charm, in an evening.
On the other hand, we don’t know how many of those spells students have to perform successfully to get a passing score. Some real-world exams are deliberately set to be so difficult that getting 60% of the questions right is considered pretty good, and 75% about as high as anyone could hope for. (I recall some of the Advanced Placement math and science exams being like this, at least about 20 years ago.) So it’s possible that students can botch quite a few spells on their OWLs and still get decent scores.
With that in mind, here’s Harry’s impression of his Charms practical: "On the whole, Harry thought it went rather well. His Levitation Charm was certainly much better than Malfoy's had been, though he wished he had not mixed up the incantations for Colour Change and Growth Charms, so that the rat he was supposed to be turning orange swelled shockingly and was the size of a badger before Harry could rectify his mistake..."
So, Harry performed one wrong, and a second—which he learned five years ago—was not confirmed as good in any absolute sense but only “better” than Draco’s. We have no idea how this compares to the rest of his practical, but he says of the Defense exam later, "Here, for the first time, Harry felt sure he had passed.” He can’t have performed that many spells successfully on the Charms exam if he wasn’t sure he’d even passed, and yet he earned an Exceeds Expectations. Though maybe he was more worried about the written section. And he did perform that wrong spell successfully, technically. So the issue might be memory, not power.
Still, it makes you wonder whether students aren’t expected to be as capable as the list of exam questions and tasks alone suggests.
Then we get the peculiar claim from Fred and George that a lot of Ministry employees can’t cast a basic Shield Charm. Not that they can’t cast very strong ones, or that they can’t react in time for them to be useful, but that they can’t cast them at all. Many of those employees would be old enough to have taken DADA shortly after the curse kicked in, when it was probably possible to find decent teachers nearly every year; some would be old enough to have studied pre-curse. Even those not much older than Harry could have formed their own study clubs and practiced. And yet that many people can’t perform one of the most basic defensive charms after five to seven years of classes?
We also hear that many people have such “woeful wandwork” that they “find [themselves] making excuses not to perform simple spells,” in the words of Kwikspell’s advertising copy. They may be exaggerating for dramatic effect, but the company exists to make a profit, and they could hardly do that if they didn’t have a large enough market. “Hundreds of witches and wizards have benefitted,” again according to the advertising copy. Within the tiny British wizarding community? Perhaps it’s the worldwide Anglophone community. Or perhaps we ought to revise their claims down a bit and assume the company isn’t as established or successful as they make out. But still.
Worse, lesson one is “Holding Your Wand (Some Useful Tips).” Just how many people within the British or even Anglophone wizarding community don’t even know how to hold a wand properly? One begins to wonder about Lupin’s belief that most British witches and wizards attend Hogwarts. Does he have credible statistics to back that belief?
And then there’s that very odd statement of Neville’s, that even after he magically bounced, his family worried he might not be “magical enough” for Hogwarts. Magical control doesn’t seem to be required for Hogwarts admission, because hardly any students develop anything resembling control over their magic for months after they start, from what we see. Why would think that anyone with enough magical power to bounce after being dropped head-first out the window wouldn’t get a Hogwarts letter? Irrational fear? Or do they know something we don’t? Maybe they know that Filch, or someone else now considered a Squib, performed some comparable magic and yet didn’t get a Hogwarts letter?
Here’s my suspicion: in fact, a large percentage of witches and wizards are magically weak, and many never attend a magical academy. Squibs aren’t as rare as the average wizard believes, either. If you asked every witch and wizard to perform a series of basic spells, many of them just plain couldn’t. Not with any amount of practice or memory-boosting tricks.
What happens is, many families have traditionally put their children through homeschooling and apprenticeships, maybe with some fly-by-night lessons from organizations which are a bit more than tutoring groups but not quite schools. So when a child doesn’t get a Hogwarts letter, or starts Hogwarts but seems too magically weak to succeed (and doesn’t have a family determined to make them succeed, like Neville’s), their family tells everyone that they want their child to learn practical skills instead of silly rats-to-water-goblets spells. Because many magically talented children also do apprenticeships and vocational programs, this isn’t automatically code for “Squib.” People who haven’t observed the child closely might honestly not know whether the kid prefers to learn practical skills or lacks magical power. No one is out gathering data, as far as we know, so even if someone knows a family trying to hide that their children are Squibs, not just working clerical or service jobs which don’t require much magic out of necessity or preference, they might believe—incorrectly—that these are rare exceptions.
The population wouldn’t be neatly split between magically weak people who don’t go to Hogwarts and magically talented people who do, because they can’t always predict aptitude (just look at how wrong everyone got Neville). But the average level of magical power is probably higher among the Hogwarts set, since Squibs don’t get in and magically weak students are probably more likely to leave early than magically strong students.
This leads to an interesting possibility. If people base their expectations of what the average witch or wizard ought to be able to do on a combination of what Hogwarts exams require and what they see people being able to do—or not—they might end up with skewed perceptions. Their conclusions might not be rigorously logical. In fact, they might be downright contradictory, if they actually sat down to work them out step by step, but when have we ever seen the average witch or wizard do that?
So they might think something roughly like this: obviously, the average witch or wizard is powerful, because look at all the hard stuff Hogwarts requires; we know that all that stuff is really hard because look how many people—including those who have never set foot in Hogwarts—can’t do those things. This muddles the abilities of two differently-defined groups: Hogwarts students who pass at least some OWLs versus the entire population.
Things get more interesting if you add historical perspective. Centuries ago, when the wizarding and Muggle worlds weren’t so separate, there would have been more wizard/Muggle marriages, producing children with a range of magical ability. Perhaps until Hogwarts got properly established—or even for a few centuries afterward—they didn’t draw such a sharp distinction between magical and Muggle. Perhaps those who would today be considered Squibs were at one point considered witches and wizards: not powerful enough to handle wands and attend Hogwarts, but witches and wizards all the same.
And what about teaching standards? They aren’t ideal in the Hogwarts we see, but if you look at the history of education, the modern situation improves dramatically by comparison. Medieval and early modern educational institutions were often extremely haphazard affairs. You’d have students roaming from teacher to teacher or even university to university whenever they chose, no set schedule or expectations, frequent riots, students going to school for years without ever quite learning to read… Why should we assume that Hogwarts escaped the social influences that produced these conditions?
Even if we assume it was better than average, a lot of students probably showed up not knowing how to read and with no math skills other than basic counting. Maybe they offered lessons which required little or no reading and writing in the past, or diverted those students into non-Hogwarts vocational programs. But maybe, at least at some points, they took the time to teach basic literacy skills and such. That would leave less time for the kids to practice magic. And if the reading lessons were quick and basic, there might have been a lot of intelligent, talented students who did poorly because they couldn’t get through the required reading or compose acceptable essays. This isn’t exactly uncommon today in more established educational systems; why should Hogwarts centuries ago have done better? It’s possible that even if, like today, the average Hogwarts student of 1300 was more magically powerful than the average witch or wizard from the population as a whole, Hogwarts students in 1300 usually couldn’t perform many more spells than the average hedge witch—as is not true today.
If some spells got a reputation as difficult because most of the magical population couldn’t perform them in 1300, when much of the magical population couldn’t even use wands and many of those who could were poorly trained, this reputation might not hold up when tested against the modern Hogwarts population. That is, it might work like this:
- Most of the magical population couldn’t perform a Patronus Charm either in 1300 or today no matter how much they practiced;
- Most of the Hogwarts student body couldn’t manage it in 1300 or even 1750, either;
- But many or most Hogwarts students today could manage it.
So we find ourselves in an odd position where magic is both harder and easier than wizards generally believe, depending on exactly who is performing it. The magical population as a whole is capable of much less than they think, but most Hogwarts students are capable of more.
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But the Ministry question is still unsolved: even sending memos requires magic, so doesn't that mean all the clerks are at least somewhat magical?
Another question: If untrained, unqualified adult wizards can own wands and carry them around openly, and attempt to use them without Ministry intervention - what's to prevent Hagrid from doing the same?
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Or maybe those jobs are reserved for those who are qualified to carry wands, if barely (and qualifying might not be as hard as they'd like us to think), and there are other, even more menial positions requiring less magic. We see a few that might fit: I don't think the witch pushing the sweets trolley on the train uses a wand that we see, and Stan and Ernie on the Knight Bus seem to rely entirely on the bus's inherent magic.
There might also be an intermediate level between "fully qualified" and unqualified. There would almost have to be, really. Otherwise you wouldn't need to specify fully qualified. Some people might be qualified only to use their wands for specified job duties, like the memo-sending if that's doable for them (and presumably at home where no one cares, not that they'd do much anyway). This would be really hard to enforce in practice, so restricted wand users probably violate the law left and right, if there is such a law. The Ministry could ignore violations when they were busy but pull someone in for "unauthorized wand use" whenever they needed an excuse or needed to meet their quotas or whatever.
Hagrid isn't just not qualified, but had his wand broken, so he's probably in a different category. He'd get in trouble if seen using a wand, because he's banned from doing that. Of course, we know that he can get away with it easily as long as he isn't seen.
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In support, we have Filch using a probity-probe to scan students for dangerous objects in HBP. We know he can't manage a wand, but he can control a probity-probe with his Squib-level magic. Perhaps a true Muggle with even lower levels couldn't, or at least not consistently.
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If he's in either of the first two categories... well, even then, the Death Eaters including Stan shows how thinly stretched they are, because there's no evidence that he's ever performed combat magic successfully. I'm not sure we see him use a wand successfully, period. If they put him under Imperius, he might be more capable than otherwise, the way Neville could perform remarkable gymnastics, but he still probably wouldn't be very effective.
If he's an unqualified wizard (who theoretically has enough magic to manage a wand but couldn't learn enough spells to pass his OWLs or equivalents for whatever reason) or a Squib, then his inclusion shows even more desperation. He would be no better than Hagrid with a wand at best, and might be worse. (Random bursts of light? Nothing? Unexpected and possibly inconvenient spells?)
In either of the latter two cases and possibly the first case (if he's a technically-fully-qualified-but-inept-in-practice wizard), his purpose would be intimidation (making the Death Eater forces look more overwhelming and hopefully panicking the Order enough that they make mistakes) and distraction (any time the Order spends aiming at Stan because they think he's a serious opponent gives the more capable fighters time to attack). Ouch. For Stan.
Or he could have secret badass skills which we happen never to see, but which the Death Eaters knew about and recruited him for... but that seems unlikely.
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Instead of Stan levitating Harry's trunk onto the bus, he and Harry physically lift it together. He also physically throws a passenger's bag out after her. Levitation is one of the very first spells they learn in first year, and so is probably one of the least difficult.
It could just be that getting onto the bus is a tight squeeze which would require precision levitation (as opposed to zooming something around a large open space), which might be beyond many wizards due to lack of coordination or other non-magical reasons. But it also allows for the possibility that Stan isn't very good with a wand or doesn't have one.
I think in GoF he's just talking, so we wouldn't expect to see a wand anyway, and in DH it's not clear whether Harry saw Stan, specifically, casting spells, let alone whether they hit anyone or did anything. There are several pursuers and spells flying in what sounds like a confused fashion, then Stan's hood slips and Harry casts "Expelliarmus" without mentioning whether or not he saw a wand in (or flying out of) Stan's hand. He may have been holding one and not doing much, or holding one and casting spells that looked flashy but did little, or casting moderately effective spells, or casting wildly successful AKs (though probably missing, or killing bats or such, given the Order's low fatality rate). But I don't think we can be sure that he did cast effective--or any--spells.
We don't see Stan enough to get really solid evidence for any particular scenario, and you can explain each instance of his not using a wand other ways, but it does it means the low/no wand use is possible in a way that it isn't for many other characters.
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Incidentally, I just looked at their meeting on the Knight Bus scene again, and Harry and Stan carry the trunk with Hedwig's cage perched on top up multiple steps into the bus. My experience of carrying large objects up stairs with a partner is that it's very difficult to hold it level, nor do you usually need or want to (which is why you don't perch unsecured stuff on top). Maybe wizard-made owl cages are charmed to stick to whatever you set them on until you deliberately pick them up? Otherwise I would expect that cage to topple or slide onto the person at the bottom, and Hedwig to express her displeasure. This is exactly when a levitation charm would be useful! Is it not possible to levitate something up a few steps and then around a sharp corner in a tight space, and if not, what is even the point of being a wizard? (I say this having recently been half of a team which maneuvered a 5-foot bookcase around a 90 degree corner and up a flight of stairs.)
Even if Stan is fully qualified and reasonably good at whatever magic he knows, he's only a few years older than Harry, and we know that by Harry's year, DADA instruction is so bad that the DA spends a lot of their existence practicing what seem like basic foundational spells like Stupefy and Expelliarmus. So even a fully-qualified, magically competent Stan might be pretty limited in a fight, unless he's a champion in those imaginary underground duelling matches where Molly honed her combat skills. They might put him under Imperius even if he did sign up voluntarily in hopes that it would boost his performance (at least by helping him not choke under pressure or something like that).
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The Wizarding world is behind the Muggle one. The idea of everybody going to school is pretty new. If you were lucky there might be a village school that teaches the basics. But "advanced" institutions were for the ruling class. So that's what Hogwarts is. Students are powerful enough to join the Ministry. Which is why all the careers we see described when the students are informed of their options are with the Ministry of Magic.
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But there's no reason most of today's wizards should know that. I doubt Hogwarts, A History explains, when we know it leaves out other important details like "who does the cooking and cleaning." If they think about it at all, they might assume the exceptional students back then who became famous were like the Hermiones of their classes, when they might actually have been the Tom Riddles (by comparison to their classmates, not in an absolute sense). And why would they think about it?
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It probably can't be a split with the more prestigious, better-paid positions requiring more magic and the less-respected, lower-paid ones requiring less, because of how much magical competence it seems like Reg the janitor's job requires. (Maybe in the wizarding world, Reg is actually better paid and more respected than the memo-charmers? Probably not if we believe the notes about Umbridge's father, unfortunately.) Percy's job--and Crouch's for that matter--doesn't seem to require much actual magic. Research, administration, event planning, interpersonal communication, yes. But this is the sort of job he wanted those exam scores for. Still, maybe it's possible to hold assistant jobs like his with a lot of good scores on the theory exams (Astronomy, History, etc.) and not great on the practicals? Though most people probably take longer to work their way up to those than Percy?
Maybe there's a weird distribution where both the highest-status and the lowest-status positions require magical skill (the first because people respect magical power and wouldn't accept a weakly-magical head of department, the second because it's all about hands-on skills), but there's a bunch of middling jobs which require minimal or no magic? All the people gathering data and writing reports who aren't special assistants, and the memo people, and whoever processes all the forms they probably receive from people signing up for Floo connections and whatever. But I couldn't guess what the percentages would be. Especially since there's a lot about their government organization we don't know.
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Arthur's job requires magic - especially Memory Charms, but he probably needs to use some combination of Charms and Transfiguration work to undo messes (such as exploding toilets). And since many of the 'pranks' he needs to undo are unpredictable he can't rely on pre-charmed devices. I'm guessing many of the jobs that have a field work component require magic, and the less predictable the task the more magical training it requires.
Hmm, there was a line in Sirius' description of Crouch about how he was very magical and that was tied to people's expectation that he would be appointed Minister any day.
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They would have needed magic for some of the jobs on their way up the ladder, though. DMLE positions in general might be likely to require magical ability--except maybe office-only support positions. (Though that's no guarantee, since I know a law enforcement guy who got tapped for fieldwork sometimes despite his actual job being managing the evidence locker.) And the DMLE seems to be the biggest and most powerful department.
What about Magical Games and Sports? Do they magically investigate rigged equipment, or is it more organizing events, setting rules, and arbitrating disputes? If they have equipment investigators, how many are there compared to positions which don't work in the field? How much magic do the people monitoring the Floo Network need to work with whatever monitoring devices are involved? Would any of the jobs Percy held in International Wizarding Cooperation (if he'd stayed there longer) have required hands-on magic, or did he need practical magical skills purely for that "great wizard" image?
True Squibs
Re: True Squibs
I wonder how easy it is for families to conceal the lack of a Hogwarts letter? What about magic just barely strong enough to get a letter but probably too weak to succeed at Hogwarts? (Well, Neville's family thought he was in this category and sent him anyway; maybe thinking you can "push" kids to be more magical is a common hope.) Rita thought that Kendra was using "delicate health" as cover for Ariana being a Squib, so maybe that's a common enough excuse that her readers would be nodding and going, "Yeah, I had a neighbor like that too, and the kid didn't seem sickly to any of us, so we all wondered..."
Presumably those who are nearly (but not quite) Squibs, and the occasional Squib whose family has managed to conceal their status, don't spend a lot of time telling their cousins exactly what they are and aren't capable of. They're trying to hide a socially-stigmatized weakness, after all. So a fair number of people could have near-Squib relatives without quite realizing it so explicitly, or how common it is. But you're right that it couldn't be so common that it's really obvious.
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Muggleborns?
It would follow that the Muggleborn students would be the only ones who would exhibit the full bell-curve of normal distribution of magical ability, whatever that might look like.
Which means that Hogwarts students would have confirmation of the Pureblood prejudice that Muggleborns are, as a group, magically weaker than those with proper Wizard blood.
Re: Muggleborns?
Now I'm imagining some Muggle-born kid starting an underground club called Lies, Damned Lies, and Statistics, where they actually study statistics and logic and things like that.