- Hey, Smart People.

Joe here.

One of the things that's always bugged me about my name is that it's so ordinary.

I mean, literally.

Since the 1800s, "Average Joe" has been synonymous with an image of the most ordinary person out there.

Which is totally unfair.

Joseph is only the 8th most popular name in the US in the last hundred years.

It should be Average Jim.

And according to people who study demographics, the most average person alive is a right-handed 28-year-old Han Chinese man who speaks Mandarin, doesn't have a car or bank account, and makes less than $12,000 a year.

His name's probably not Joe either.

In fact, when it comes to height, I'm above average for male Americans.

I'm above average in fitness, too.

But I'm a below average break dancer.

(upbeat music) I'm also a below average knitter.

And I'm a stunningly average chess player.

Before all you armchair grandmasters make fun of me, chances are YOU are pretty average at a lot of things too.

Because when you look at how many measures or data points tend to be distributed among a group, you're more likely to be closer to the average.

Averages are all around us, but we have a hard time comprehending them.

There was one study back in the 80s, 93% of Americans said they were safer behind the wheel than the average driver.

That's impossible.

That's not how numbers work.

But maybe we could wrap our heads around this idea a bit better if we expand our horizons beyond thinking about common stuff like height, or ability, or age, and things like that.

What if we consider everything?

What is the most average thing?

(upbeat music) Averages affect our lives every day, even if we don't realize it.

For instance, houses are built for adults of average height, shoes are made to fit the average-shaped foot, car crash tests are mainly done on dummies of average male and female body size, and airplane seats are designed to fit the average person comfortably.

Okay, nevermind on that last one.

That's just torture.

When you dig into the world of averages, one of the first things you realize is there's more than one way to be average.

So before we start this little hunt for the most average thing of all, we've gotta figure out what it means to be average in the first place.

To the dictionary.

The dictionary defines average as "A single value that summarizes or represents the general significance of a set of unequal values."

Okay, that sounds annoyingly vague.

So it's something general that gives us an idea of a set of values.

But when we say something is average, do we mean it's the most common, or that it's right in the middle of a range of different values, or is it the value that most represents kinda the general vibe of the group as a whole?

Because sometimes those are the same thing, and sometimes they're not, and sometimes they're something else altogether.

So if we're gonna find the most average thing in the universe, first we have to figure out which average we're talking about.

There's a fancy term for this one value that represents the entire bigger group, and it's called the central tendency.

And the three most common ways to measure that central tendency are mean, median, and mode.

But depending on which one you use, you can get a different answer.

Like let's say you want to know what the average income is.

Well, you could add up all the numbers and divide by the number of working people.

That would give you an answer.

But then, maybe one of those people is Jeff Bezos, and his income is so ludicrously big compared to the others that the average you get isn't really a useful answer to the question.

Billionaires.

Always trouble.

Luckily, we've got other ways to measure that ol' central tendency.

Let's start with mode and median.

If you wanna figure these out, you need a lot of data.

The mode is the most commonly occurring item in a data set.

In order to find the mode, you'll need a list that includes every single thing that you're trying to analyze.

Let's look at the greatest basketball team of all time: the 1992 USA men's team, AKA the Dream Team.

Indisputable scientific fact, don't @ me.

If we want to figure out the mode height of the players, we'd list each player and their height, then find the number that appears most often.

The answer is 2.06 meters.

In SI units this is also known as one Larry Bird.

But what if we wanna find the median height of the players instead?

Unlike mode, the median is like if you took a set of data, laid it all out in order, and picked the literal middle.

In this case, the median player height would be a bit more than a Pippen, not quite a Bird.

You'll notice that the median height is not actually in our data set, and that's because we have an even number of players in this dataset.

If we added one more, the median would be ol' Scottie.

Now, for a fairly small data set, these are pretty trivial.

But if you wanna find the median or mode thing in the universe, say, by size, then we would need a list of the size of every single thing in the entire known universe, which is so impossible.

I can't even talk about it without my head hurting.

That's referred to as finding the arithmetic mean.

That's the thing you do where you add up some values, divide by how many values there are, and you get that general vibe number.

The average you probably still remember from school.

Mean is the average in batting average, or average rainfall, it's the average most people usually have in mind when you think average.

The arithmetic mean can help us find the average of all sorts of things, like how many people make up the average family in the United States.

And the great thing about it is you don't necessarily need to look at the whole set of data to find it, you just need some representative subset of the data.

That way, we can use a small number of things we know to calculate the average number in that immensely larger set of things that we don't necessarily know.

We just need some subset of data that accurately reflects the whole, some limits, like say, looking at data recorded between 1960 and 2021, and we can come up with a central value that tells us the average.

It's 3.13 people, by the way.

(laughing) We can also find even more important means, like the mean age of the Dream Team, 29, the mean number of points they scored during the 1992 Olympics, 121, and the average point differential between the Dream Team and their opponents, 51.5.

Boom, best team in the universe.

(crowd cheering) And speaking of the universe, we should get back to finding the most average thing in it.

Now that we understand the different kinds of averages, we can figure out what kind of average we're looking for.

Median and mode would be useful, because these types of averages don't get skewed if there's some really big or small outlier value, like a Bezos galaxy cluster or something.

But on the other hand, they would require cataloging every individual thing in the universe, and I don't really have time for that.

See, yeah, I've got a thing in an hour, so we can keep the process simple by using the smallest thing in existence and the biggest, and then calculating the middle between those two, even just to an order of magnitude.

A simple mean between two measures.

Okay, this seems straightforward, except what do we mean by biggest and smallest?

For instance, if someone asks how big New York City is, do they wanna know the area measured in square kilometers?

And are we talking about New York City's land mass, or do we include the waterways within New York too?

Or maybe they're not talking about the area at all and wanna know how many people live there instead.

So, in reality, size is all a matter of perspective.

It's about how we choose to measure something.

There are seven internationally recognized basic units that we can use to measure stuff.

These are known as SI units.

Only two base units quantify something's size.

The first is kilograms, we can use to measure an object's mass.

The second is meters, which helps us quantify length or volume, which is the amount of space a three-dimensional object occupies.

That's a lotta definitions for a video about math, huh?

Now, anything with a measurable size will have both volume and mass.

But each of these gives a very different answer for what might be an average size.

For example, if we ask what the biggest and smallest stars are to calculate the mean, we would end up with different answers depending on whether we're talking about mass, the amount of stuff in the star, or volume, the amount of physical space that the star takes up.

On one hand, a neutron star might take up thousands of times less physical space than our sun, but be hugely more massive by having more matter inside of it.

So depending on whether we're using mass or volume as our base measurement, that star could be bigger or smaller than our sun.

Anyway, we've gotta pick one.

Otherwise we'll be here forever.

We're going with size in meters.

Again, not freedom units, because this is science, and because that powers of 20 arrangement is really gonna come in handy in a second.

All right, awesome, we're ready to roll then, right?

Time to bust out those calculators, except, not quite.

Because now we have to figure out what we mean by a thing.

If you thought that we'd opened a can of worms when it came to defining averages and measurements, well, trying to define what a thing is, is like opening a whole truckload of cans of worms, except the worms are all philosophers and all they seem to do is ask questions and argue about what words mean.

So instead of pulling on that thread and unraveling the entire universe and our sanity along with it, let's just say that a thing is an organized structure that's made of matter and held together by the universe's fundamental forces.

Not today, philosophers.

So what is the smallest thing in the universe that we can measure in meters?

We can start by thinking about the smallest things that make us us.

Eukaryotic cells are the basis for organisms like plants and animals.

Measuring in at roughly between 10 and 100 millionths of a meter in diameter.

But cells are obviously made of smaller things, proteins, nucleic acids, all kinds of different molecules.

And those molecules are composed of atoms.

Atoms are what many people think of as the basic building blocks of all matter, and we measure them using angstroms.

An angstrom measures in at 10 to the minus 10th of a meter, or 0.1 billionth of a meter.

All atoms are in the neighborhood of one to two angstroms in size.

For a little perspective, it would take 50 million atoms all lined up in a row to make up one centimeter in length.

But atoms are not the smallest things in the universe.

They are composed of even smaller bits and bobs called subatomic particles.

Inside every atom is actually mostly empty space, but at the very center, tens of thousands of times smaller than the atom itself, is the teeny tiny nucleus, composed of protons and neutrons, and around this nucleus is a cloud of electrons.

That means that protons, neutrons, and electrons are insanely tiny.

Electrons are the smallest of all, with a radius in the neighborhood of 10 to the minus 15 meters, or quadrillionths of a meter.

But electrons are not the tiniest things in the universe either.

It turns out that subatomic particles come in different flavors.

Sure, neutrons, protons, and electrons get the most press.

But there are other, even smaller ones, too.

For instance, bosons are particles of force, but without matter as we think of it.

Photons, which are particles of light, are bosons.

So is the Higgs Boson.

It's right there in the name.

Fermions, on the other hand, are subatomic particles of matter.

There are a bunch of different types of fermions, like leptons, baryons, and these things, quarks.

A quark is the smallest building block of matter that we can actually detect and measure, at least right now.

So, we've finally arrived at the smallest thing in the universe, a quark, which comes in at about 10 to the minus 18 meters.

But these are just the smallest particles we can measure.

Our current models of physics tell us with pretty good certainty that there are even tinier particles out there called neutrinos.

But for our calculation, we're sticking with the quark because we can actually determine its size, one quintillionth of a meter, or one attometer.

A one with 17 zeros in front.

That is small.

Now, we've gotta find the biggest thing in the universe.

Since we're looking for the biggest thing held together with a fundamental force, it might be the whole known universe.

That's because Einstein's Theory of General Relativity states that gravity is the invisible structure that holds all of space and time together.

The visible universe is roughly 93 billion light years across.

And that's expanding and getting bigger all the time.

But we're looking for something that has structure, or a pattern of organization.

And frankly, we have no idea if the whole universe, like all of it, has any larger pattern of organization.

It's kind of a mess, to be honest.

Organization and actual structures likely only start at smaller scales.

Galaxies have structure, like this one.

So do galaxy groups, like this one, or this one.

But there's an even bigger thing out there with a definite organized structure, these clusters of millions of galaxies, known as galactic filaments.

The largest known galactic filament is this beauty, the Hercules-Corona Borealis Great Wall.

It's 10 billion light years across and contains just oodles of individual galaxies.

But there's a lot of empty between the galaxies and stars and other stuff that makes up a galactic filament.

It turns out there's a good reason they call it space.

We're looking for the biggest object that operates as one thing without tons of space between each of its pieces.

And that leaves us with, drum roll, please, this guy, UY Scuti, the largest star that we know of.

It kinda looks like its name should be UY Scuti.

This hypergiant star at its largest point has a radius of roughly 1,700 times that of the sun, and a diameter of about 2.4 trillion meters.

This means that if you put its center where the sun sits in our solar system, its furthest edge would fill all the way up to Jupiter's orbit, or even Saturn's maybe.

That would not be great for Earth by the way.

Now, it's finally showtime.

We have our smallest thing, the quark, and our biggest thing, UY Scuti.

I mean, UY Scuti.

So our largest star at 2.4 times 10 to the 12th meters in diameter, the quark at 10 to the minus 18th meters.

We find a power of 10 at the middle between these two numbers, adding 12 and 18, dividing by two, and you're at 10 to the minus three meters, about a millimeter.

You know what's about a millimeter in size?

A tardigrade.

Yeah, those cute little pudgy water bears everyone's always going on about.

Well, I've got news for you, they're the most average thing in the universe.

There, I said it.

Now that I've said it, I'm actually not sure if this new title makes them less special or more special.

But remember, this only counts as an answer if we're thinking about the average size in meters of everything, ever.

And that's just one kind of average.

Like, the average would change if we tried to figure out what the most average thing in the universe was in terms of how many of them exist.

Spoiler alert, there's only one UY Scuti, but there are more than one vigintillion quarks.

That's a real number.

So, if you wanted to find the mode, the most frequent value in this data set of everything in the universe, it's gonna be skewed by the thing that there are way more of.

And the average thing then would basically be quark.

The thing is, when most people think of averages, they are picturing all the things in a set, put together, and then we figure out what this point is, the mean.

But that's just not something we can do for every data set, especially one where it's impossible to have all the data, like the universe.

In reality, there's a whole multiverse of possible averages, and different averages tell different stories.

So use them wisely.

Since you've made it this far, I'm going to tell you what I think the weirdest middle of them all is, we're all the middle of our own universes.

Like, I'm in the middle of everything I can see from here to the edge of the observable universe 46 and a half billion light years in any direction, and you're in the middle of your own observable universe that stretches the same distance in every direction.

So I'm a middle, you're a middle, and it's different from everyone else's middles.

So when it comes right down to it, being average, or right in the middle, is all about perspective.

And our relationships to objects, to space, even to each other.

So if you ever feel average, or stuck in the middle, maybe all you need is a change of perspective.

Stay curious.

Hey, thanks, friends, for watching this video and learning some pretty cool stuff with us.

There's a link down in the description to our Patreon, where you can support the show directly, which is pretty cool, and we would really appreciate it if you checked that out.

Just get on down there, and while you're there, go ahead and make sure that you are subscribed, that you've given this video a little like, you know, all that usual stuff.

You can even leave a comment, I'll probably read it.

And I'll see you in the next video.

It should be UY Scuti.

I like that better.

UY Scuti.

That's not how we say that.

Let's make a video.