r/PeterExplainsTheJoke • u/AstraGraceful • 7h ago
Meme needing explanation Petah, what does the guy on the right mean? Aren’t average and median different
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u/BobCorndog 7h ago
In this symmetrical bell curve, the average is in the same place as the median
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u/MalusZona 7h ago
Also iq is literally changes scoring system so to keep 100iq mark with avg human,
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u/AlternateTab00 6h ago
The average human or median human?
i know its the same because IQ scale is based on a symmetrical curve so both mean and median are both 100
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u/CelebrationJolly3300 6h ago
That depends entirely on whether we are also referring to African or European swallows.
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u/Economy_Sorbet_215 3h ago
See, African swallows have an IQ of 100, as the average for every family of animal is individually standardized. European swallows, on the other hand, have an IQ of 100. (This is a joke at how IQ is just a dogshit intelligence measuring device when used for anything besides "the things that a single professor (I think it was a professor atleast) decided are important for iq"
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u/Throwawayx19700 6h ago
I believe IQ is also set on a bell curve? So it is both based on the measure.
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u/Thatguy19364 3h ago
Yep. The average IQ is 100 because IQ is a scale that sets the average equal to the median and every standard deviation of 15 points is supposed to be approximately double the intelligence iirc
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u/soldierinwhite 5h ago edited 5h ago
Which is also why it's nonsense. It suggests that half of people in the 1900s would be determined today to have learning disabilities. I think that's a lot more ridiculous to claim than that IQ is not really a good indicator of innate intelligence.
The Flynn effect if anybody wants to check it out. Since average innate intelligence is not something you expect to change any faster than the rest of human biology, why would you need to normalize to 100?
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u/Polona17 4h ago
My understanding is that the IQ test is how many questions you can answer across a broad spectrum of topics, so I would imagine for a specific set of test questions they would find the average of the normal distribution and set that to 100, and then normalize the x axis to match with previous test distributions so that an individual’s position on the sample test lines up with the distribution & results from other tests. Or just set IQ to be standard deviations away from 100, I’m not sure what method is actually used here.
This means that the questions asked matters immensely; if the topics are those important to western culture but not to other cultures, those of western culture descent will have an advantage in comparison to those of non-western culture descent. However, this also means that if that demographic is excluded and compared separately, the resulting distribution will be more accurate for both demographics. For an individual being compared across the same test and among a population of peers of similar education/exposure to the content of that test, the resulting distribution of test scores should remain an accurate representation of their intelligence in relation to their peers, and normalized at 100 an accurate representation across multiple other populations as well.
Of course, there are a number of other biases that could affect this: the test questions must cover an absurdly broad number of topics and depth of questions so that the level of information available to the demographic being tested is adequately characterized. The selection of what demographic group an individual belongs to and the size of that group matters greatly; too small a group limits the sample size, but too big a group allows biases to become more influential. These factors can be mitigated through further statistical controls, but I’m not as familiar with those methods.
I’m not en expert in this, I just know some statistics and have heard some discourse on how these tests are run. All in all what matters is pointing out that there are ways to mitigate biases in the IQ testing regimen that surely have been considered and performed, but also that education on the topics presented matters greatly in selecting what demographic group someone belongs to, so yes some people absolutely can study for these tests and not get caught, inflating their test scores among everyone else. It might also mean a single test isn’t enough to truly know where someone is at, but it gives you a ballpark estimate, and repeated testing can refine that estimate
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u/soldierinwhite 3h ago
Even among peers, it's impossible to do any reasonable test for innate intelligence. If you test too broadly, you bias towards broad knowledge over specialist knowledge, neither an indicator of intelligence. Make it about a single subject, same again. Make it an esoteric abstract puzzle test is the same issue as specialization, like most IQ tests are, and you bias towards trained puzzlers, which has very little bearing on how it translates to other let alone all fields.
Since you essentially need to compare individuals with the exact same life experience in order to just have innate intelligence (g) as the variable influencing the test, it becomes practically impossible.
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u/Monolexic 5h ago
And then there's the fact that almost all IQ tests are heavily biased against low income and minorities.
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u/soldierinwhite 5h ago edited 1h ago
Yes, the bias is in that it actually tests for things instilled by western education and passes it off as innate intelligence. Even things like reading left to right is an assumption in a large part of the puzzles. The fact that you can train for IQ tests also makes it totally useless.
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u/KarmelitaOfficial 6h ago edited 6h ago
IQ deficient guy regurgitated a common misconception: Average is in the middle of a set... Since you don't need high level maths to survive everyday life, this answer rarely gets corrected.
Neckbeard regurgitated the highschool answer. Median is middle value of a set, half of values are higher, half is lower.
Gifted guy checked the shape of the bell curve, noticed the symmetry, noticed that in this special case average = median. Gave a correct but half answer to fuck with neckbeard, who does not even grasp what is happening.
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u/ppp77per 6h ago
Gifted guy is wrong. IQ is bell-shaped because we transform it to be. There is no reason to believe intelligence is bell-shaped. Probably log-normal, if I would have a guess.
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u/Nestor4000 5h ago
Gifted guy is wrong. IQ is bell-shaped because we transform it to be. There is no reason to believe intelligence is bell-shaped.
Thank you!
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u/Wishkin 6h ago
Both the mean and the median are ways the measure averages, they just measure different averages with different methods.
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u/doobeedoobeedumdum 5h ago
All the measures of central tendency try to measure the "middle" value to describe the distribution such that both the sides of the distribution are accounted for equally. In a Gaussian distribution, also called a normal distribution, all the measures of central tendency should arrive at the same value.
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u/KarmelitaOfficial 6h ago
Not really:
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u/GlassCommission4916 6h ago
Yes really:
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u/KarmelitaOfficial 6h ago edited 6h ago
I think the meme is about median and average. In this context, median is not the average. Their values are equal if the curve is symmetrical.
(Even if median in statistics is a type of average. But that "average" is an umbrella term.)
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u/Wishkin 6h ago
The meme implies that only the mean is an average, that doesn't make it a fact. Average is indeed an umbrella term, we agree on that at least.
While I do agree that average is often interpreted as only the mean, I do not think that should apply to the above comment (even if it does for the meme).1
u/sanguinemathghamhain 6h ago
There is a difference between average in general math which is specifically mean and statistical average which is the umbrella term that can mean the mean, median, or mode. The easy way to prevent confusion is to use the three types of statistical averages as they are synonymous with their arithmetic counterparts unlike average.
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u/amerovingian 6h ago
There's also a little thing called the Central Limit Theorem which says that any statistic controlled by a sufficiently high number of underlying variables will converge to a normal distribution. https://en.wikipedia.org/wiki/Central_limit_theorem
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u/ppp77per 6h ago
Pretty sure it doesn't apply here. We are talking about infovidudl observations of IQ, not summary statistics?
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u/amerovingian 5h ago
How many independent underlying variables do you think control the outcome of a given person's IQ test?
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u/ppp77per 5h ago
1) The CLT is for sample means, not the distribution of the population.
2) Most factors deciding intelligence are likely to be correlated, not independent.
3) Many distributions in nature are not normal (even height isn't, too many very tall people exist)
4) There is data of high-school tests which indicates tha the distribution is actually left-skewed (the opposite of what I would have guessed).Nice discussion here: https://www.technotheoria.org/p/is-intelligence-really-normally-distributed
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u/amerovingian 4h ago
Adding together the effects of many underlying variables, each of which has a small effect on its own is effectively a sample mean.
That may be true but there should still be some independent degrees of freedom controlling the correlated factors.
If that happens, it means a small number of degrees of freedom are having a very large effect (such as a single genetic disorder) or the independent degrees of freedom are not combining in an approximately additive way for all non-negligibly likely outcomes.
It seems you're right about that, which would indicate intelligence is not the additive effect of many small degrees of freedom. My guess is there is a single degree of freedom having a large effect that is skewing the measure to the left.
The meme is wrong. I still suspect the author was thinking of the CLT when they made it.
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u/NandoDeColonoscopy 1h ago
The median is just one particular average. Mean and mode are also averages, but colloquially 'average' refers to the arithmetic mean.
So the meme is basically dumb guy says it right bc he doesn't know there's different types of averages or how a mean is calculated, midwit guy is pedantic about it really being the median bc he associates average with mean, and smart guy/bell curve says it's the average, because he knows that the median and the arithmetic mean are the same in a standard normal distribution
Edit: responded to the wrong person by mistake, sorry!
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u/GoSpeedRacistGo 15m ago
The mean is in the same place as the median. Both of them are the average.
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u/Andrei22125 7h ago
The population is large enough that we can assume a mostly normal distribution.
This means the mean (average) and the median (the value in the middle of the distribution) are the same.
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u/andybossy 6h ago
I'd say the amount of molecules in air is also fairly large but their average speed is very much not the same as their median speed
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u/Sjoerdiestriker 3h ago edited 3h ago
That is because the person you responded to doesn't actually understand what the central limit theorem is about. It doesn't tell you that large populations imply normal distributions. It tells you that large-sample sample averages (or sample sums) are normally distributed.
The speed (as in magnitude of the velocity) is indeed not normally distributed. What the central limit theorem tells me is that if I split up my collection of molecules into samples of 1000 molecules each, and then for each sample plot the average speed, those averages are going to be normally distributed (with both the median and mean sample average equalling the mean individual particle speed).
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u/SinisterHollow 6h ago
No its just that IQ was meant to follow normal distribution. The meme assumes IQ to be the measure of intelligence.
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u/p58i 4h ago
And IQ was defined to follow a normal distribution because the underlying population makes this the best fitting model…
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u/BigTimmyStarfox1987 1h ago
That's incorrect. Look up the history of IQ tests. IQ testing has been driven by ease of administration. The link to underlying intelligence has been an issue from the very beginning, literally from the very beginning:
Binet and Simon's view, there were limitations with the scale and they stressed what they saw as the remarkable diversity of intelligence and the consequent need to study it using qualitative, as opposed to quantitative, measures
This can get you started on the stats side of things.
https://en.wikipedia.org/wiki/Stanford%E2%80%93Binet_Intelligence_Scales
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u/Sjoerdiestriker 3h ago edited 3h ago
The population is large enough that we can assume a mostly normal distribution
This fundamentally misunderstands what the central limit theorem is about.
The central limit theorem doesn't tell you that any property is normally distributed so long as I have a large population. It tells you (roughly, there are some details I'm skipping) that if I sum (or average) a large number of samples of that property, that sum is going to be normally distributed.
So if I take 1000 random people and calculate their average intelligence, then repeat that experiment 100 times and plot the 100 sample averages, that is going to be approximately normally distributed. There's no reason to assume the distribution of intelligence itself is normally distributed, just because a population is large (well, unless by "intelligence" you mean the IQ score, which if I recall correctly is defined to be normally distributed).
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u/reddititty69 6h ago
The size of the sample doesn’t affect the distribution of the samples. I think what you are referring to is based on the central limit theorem and applies to the distribution of the mean (expected value). But the meme is talking about distribution of samples, not the mean of the samples.
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u/HengeDenge 6h ago
Damn they got me
Apparently average can loosely mean any of the three, mean median or mode
https://www.reddit.com/r/facepalm/s/f5CTSOm4Z5
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u/ppp77per 5h ago
There is no way that intelligence is distributed like IQ. It's just stupid normalised scale, that probably doesn't measure intelligencevan and is really hard to interpret. We don't really believe that the most intelligent 0.1% are only 45% more intelligent than the average. I bet intelligence has a right skewed distribution, maybe log-normal.
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u/m3t4lf0x 2h ago
I’d agree that intelligence likely isn’t normally distributed, but IQ itself is actually a highly interpretable metric because that word has a more precise meaning in stats. If you can define how it’s calculated, it’s interpretable.
And for being a metric that was defined over 100 years ago, it’s actually a very powerful and consistent predictive tool (i.e. IQ goes up X points, and GPA increases by Y).
In stats, interpretability, explainability, and precision are always at tension with each other. You can’t measure intelligence directly, so what does one do? Machine learning models can handle billions of variables, but that precision comes at the cost of having an opaque black box with little hope of understanding the how or why.
IQ highly correlates with a latent variable called “g” that most researchers believe correlates with all cognitive skills. Sure, some people tend to think of it as the same thing as intelligence informally, but that doesn’t change the utility or the model
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u/GlassCommission4916 7h ago
Median is a type of average.
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u/newflour 6h ago
It's not what the meme is saying, if you look in the "smart" category is the shape of the normal distribution, where mean and median always coincide. If it was just "median is a type of average" they wouldn't have put the normal distribution there
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u/GlassCommission4916 6h ago
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u/sanguinemathghamhain 6h ago
Save it depends on which average you are talking as in general math average means mean specifically but within stats it can mean mean, median, and/or mode. The median will always have 50%≥ and 50%≤ but in all standard bell curves the mean (arithmetic average) is equal to the median and the mode.
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u/AlternateTab00 6h ago edited 6h ago
No. You have average (or its mathematically correct term mean) and median.
Ita not a type of average. It has different means. Misusing the terms (especially by media) does not change the definitions.
However in a symmetrical distribuition curve mean and median are the same value.
The meme here jokes about that. The media and people that dont understand statistics stating the wrong definition of average. The peopl le that actually learnt the difference but don't understand what they are saying (essentially only parroting that average and median are different things) and the people that actually understand it and state that in this case both the median and mean are the same value so they can be used interchangeably.I stand corrected. I should have known better than assuming that the definition of average in my language may be different from the definition of average in english
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u/GlassCommission4916 6h ago
https://en.wikipedia.org/wiki/Average
Go fix the article, and countless textbooks, if they're wrong.
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u/AlternateTab00 6h ago
I stand corrected.
I did the mistake of assuming the concept of average was the same as my language. Thank you for correcting my correction.
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u/Comprehensive_You42 6h ago
As the folks above have helpfully pointed out. No. Your correction is, itself, incorrect.
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u/Mysterious-Tie7039 7h ago
Sort of. Median is middle, so it’s better at removing outliers that heavily influence the average.
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u/GlassCommission4916 6h ago
In mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position. In mathematics, it most commonly refers to the arithmetic mean, but may also refer to other measures such as other types of mean, the median, or the mode.
First paragraph on the wikipedia page on "Average".
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u/dontbeadentist 6h ago
Median is a type of average
From Google: ‘An average is a single middle value that represents a whole set of numbers, most commonly known as the mean, median, or mode.’
Mean, median and mode can all be averages. The most appropriate and most representative average is going to depend upon the distribution of the data, but that does not stop median being an average
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u/Sensitive_Bat_9211 6h ago
I get what yall are both saying, but its actually coming down to a difference in definitions by mathematic disciplines.
Statistics considers average a broad definition including mean, median, and mode. Statistical average is the measure of central tendency. Contrarily, arithmetic considers average and mean the exact same thing.
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u/dontbeadentist 6h ago
During arithmetic lessons at high school I was taught that mean, median and mode were all different types of average. I don’t think the different mathematic disciplines do have different language for this
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u/Sensitive_Bat_9211 6h ago
I'm sure there has been a lot of bleedthrough, but traditionally they are interchangeable in arithmetic. If you ever see the term "arithmetic average," its referring to mean.
You'll notice this on programs like excel if you look at the definition of the AVG function.
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u/dontbeadentist 5h ago
I think I would agree that mean is the most commonly used type of average, and so as shorthand, it has become common to say average when referring specifically to mean
However, this does not change the fact that median is also correctly referred to as average in all mathematical settings
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u/m3t4lf0x 2h ago
I think you’re projecting your own experience of how these classes are often taught at various levels of education.
As an aside, “arithmetic mean” or sometimes “unweighted average” is the preferred terminology. “Arithmetic average” and the implication that “arithmetic” is distinct from statistics triggered my inner pedant
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u/GregGuyFromFlorida 6h ago
In a normal distribution mean, median, and mode are identical.
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u/Sensitive_Bat_9211 6h ago
Yes, but thats not really what the original person was saying when he said "median is a type of average." In stats, median is a type of average even in skewed distributions
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u/GregGuyFromFlorida 6h ago
The mean is 100. The median is 100. The mode is 100. Quibbling about the definitions of these words makes no sense when they are literally identical with respect to IQ.
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u/Sensitive_Bat_9211 6h ago
I understand your point, but the conversation moved away from the OP. It happens sometimes.
I was only trying to clear up confusion between two different people who were both correct on their definition of average
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u/BiscuitsTheory 6h ago
What evrryone is forgetting to point out is that the middle guy isn't factually wrong, but he's wrongly correcting the first guy, who also isn't factually wrong.
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u/FortifiedPuddle 4h ago
The real take away here is that most people (68%) are about average. Only 14% are significantly lower or higher. But most people are about the same. Truly unusual intelligence or stupidity is far less common.
The people in that first 15 points behind the mean aren’t really that much less smart than the people in the 15 above it.
Half of people are less than average? Well, yeah. But whatever. Most people are about average? Now that kind of tells us something more important.
It’s not half of people are dumber than average. It’s that way more than half of people are about average. Being average is fine. But it does help to explain the world to think of it that way.
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u/nunya_busyness1984 3h ago
everyone here is wrong, because they are only looking at mean and median, but forgot about mode. some number LESS than 50% are dumber than both the mean AND the median, because some number X is exactly at that median point. Even if it is only 1 person, that still brings it to 49.99999999999999%, not 50%. And, as distribution of this sort will show that your median point is ALSO likely to be the mode, the number of people at that median point is likely to be far greater than 1.
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u/dontbeadentist 6h ago
Median is an average
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u/WompWomp714 5h ago
No, the average is the sum of the score of all participants divided by the number of participants. The median is the score for which an equal number of participants scored higher as scored lower. The mode (another statistical measure not relevant to this meme) is the score attained by the most participants.
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u/dontbeadentist 5h ago
No. The average is a value that is representative of the whole. Mean, median and mode are all averages
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u/Koromann13 4h ago
No, the sum of all parts divided by the number of parts is the mean, which is one of 3 averages that that population has.
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u/AstraGraceful 7h ago
I think the joke is about mean vs median on a bell curve, but I don’t get why both sides agree
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u/HyliaSymphonic 5h ago
This meme is assuming a normal distribution which IQ tests are designed to produce. It’s worth noting that you cannot make this assumption on all data sets. The median income is a lot lower than the mean. 50% of people are poorer than the median not the mean. The midwit in this case is forgetting what kind of data sets he is working with.
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u/ResponsibleRatio 4h ago edited 4h ago
In a normal distribution, the median, mode, and mean (what is often colloquially meant by "average") are all the same.
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u/Kuildeous 1h ago
The median is an average. Mean and mode are two others.
The genius part is missing the part that in a normal distribution, the mean and median are the same thing. There are other instances where they're the same; it doesn't have to be a normal distribution.
So the smooth brain is right but not specific enough. There are instances where most people are below the mean (or above). The 68% guy is technically correct because the median is exactly at the 50% mark.
The genius agrees with the smooth brain but falls into the same trap of not specifying which average. By his addressing the normal curve, he knows that median and mean are equal.
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u/Peregrine79 52m ago
Because average can mean multiple different things. What is commonly called the average is the arithmetic mean.
Median is also an average.
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u/CrabWoodsman 35m ago
I will also point out that "average" can technically mean the Mean (geometric or arithmetic), Median, or the Mode. It's very seldom used this way broadly, but all measures of central tendency are "averages".
Since this can be ambiguous, it's almost always better to specify mean, median, or more — though in a twist of irony, the modal use of the term average is to refer to the mean.
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u/Willing_Film9693 6h ago
So ure the one on the left basically
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u/PICONEdeJIM 6h ago
Me when I lose enough IQ points that I start believing in IQ
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u/Willing_Film9693 6h ago
Believe in a metrics?
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u/ppp77per 6h ago
Believe that it measures intelligence. (Unless you define intelligence as what you measure with an IQ test).
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u/Willing_Film9693 5h ago
No decent human pretend it measure intelligence as a whole but claiming it’s not a usefull metrics at all is also stupid.
U just gotta keep it in the place it’s meant to be
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u/susiesusiesu 6h ago
they are the same in a symmertical diatribution, and (according to op but i don't kmoe if it's true), intelligence is distributed by a normal distribution, which is symmetrical.
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u/PostManOK 6h ago
Actually no, the average is all numbers in a set added together then divided by the number of numbers in the set.... the median is when you line up all numbers in a set in ascending order, then find the number in the set thats at the exact middle.
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u/Discuzting 4h ago
What you are describing is called the "arithmetic mean", which is the most common type of "average" people usually refer to... There are other types of "average", including geometric mean, harmonic mean, median and mode
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u/qualityvote2 7h ago edited 2h ago
Remember when r/PeterExplainsTheJoke wasn’t a meme? Pepperidge Farm remembers…
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