Mean, Median, and Mode: Measures of Central Tendency: Crash Course Statistics #3

Today we’re going to talk about measures of central tendency - those are the numbers that tend to hang out in the middle of our data: the mean, the median, and mode. All of these numbers can be called “averages” and they’re the numbers we tend to see most often - whether it’s in politics when talking about polling or income equality to batting averages in baseball (and cricket) and Amazon reviews. Averages are everywhere so today we’re going to discuss how these measures differ, how their relationship with one another can tell us a lot about the underlying data, and how they are sometimes used to mislead.
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[@Faith-xv9vo]

The fact that crash course is free is such a blessing

[@thatisjustgreat]

Statistics has it's moments. The mean is one of them.

[@rparl]

thatisjustgreat I see what you did there. The mean is the first moment? I hope she'll get into moments. I had forgotten about them until you brought it up.

[@SanvelloSerapiega]

thatisjustgreat I don't know, the mean is kinda average

[@samueldravis7865]

+

[@MisswhitebirdNL]

The first one in my opinion

[@timtran9563]

Statistics are currently my favorite field of mathematics.They can be very easily applied, and best of all, they can really help me understand a situation. I feel as though statistics have really helped me make better decisions in my life, and in some ways, made me a smarter individual. Thank you Crash Course for making these truly enlightening videos.

[@bluon259]

Mode - Most Median - Middle Range - Subtract the smallest from the largest Mean - Add and count and divide This is a little song I learned in the fifth grade. Huh. I didn’t know it was statistics.

[@luciofernandes366]

Oh god I'm watching for fun a class that I hated

[@abdellahdany1689]

Lucio Fernandes same here hahahhaha

[@ran88dom99]

the end of school as we knew it

[@EdSchroedinger]

according to the distribution, the median benefit you could take away in 'bad' (or boring) statistic classes is lower than the mean knowledge to take away, taking the 'good' (or enjoyable) CrashCours episodes into account as well... so, that distribution is certanly skewed due to those great episodic mode peaks... learning can be so much fun :D

[@mickeymoose636]

im taking statistics next year so im glad this is coming out now

[@zareh805]

Lucio Fernandes same

[@graciestrawser6630]

This series is great! I'm a college student who is taking Introduction to Statistics, which can be difficult because my algebraic understanding doesn't go past Algebra II, which I took 3 years ago. This series PERFECTLY aligns with what I'm learning in my statistics course, and it couldn't be more helpful. Thank you so much for all your hard work!

[@GladysSpume]

This is a fantastic introduction. I'm not a mathematically minded person, but am about to embark on a project that will require statistical analysis and this has been the best introduction I've found. Thank you!

[@haikohuvenaars]

"As soon as Musk walks into the room, the average income skyrockets", I see what you did there..

[@lucash8858]

Very useful analogies - Adrienne is doing a great job so far!

[@ShawnRavenfire]

This is a huge pet peeve of mine. I keep hearing politicians saying that the "average" income is rising, and I'm always like, "Mine isn't!"

[@Pfhorrest]

This is really helpful for understanding the inequality of income. For US personal incomes, the mean is about twice the median, but the mode is barely over half of it. That is to say: about 50% of Americans make half or less than the average income, and the largest group of Americans make only a quarter of average. Because most of the income is concentrated in a tiny number of hands. A total of about 75% of Americans makes less than average. Yes, most people make below average. We are all fucking poor.

[@arnoboy96]

Pfhorrest this

[@douglasmagowan4918]

The vocabulary of central tendencies is really bad for the income discussion. There is no "central tendency." The language of statistics was developed to describe the normal distribution. But income is not normally distributed. Income follows a Pareto distribution. There are a lot of people who make nothing, and few people at every income level thereafter. It is all one big tail. The length and shape of that tail is ultimately more meaningful than anything that is supposed to be representing the center of mass. A lot of things follow this Pareto distribution. The brightness of stars, the energy released in earthquakes, the populations of cities. Nearly everything that doesn't have a physical reason capping the top end. The Pareto distribution is associated with the 80/20 rules. 20 percent of the your workforce is responsible for 80 percent of your profit.

[@AStrangeTree]

Speak for yourself! *eloquently sips cup of tea*

[@ran88dom99]

average =mean . how do you group? I mean what are the bin sizes?

[@aronlinde1723]

The biggest problem isn't the math, it's the relative language which is attached to the values. Poor is a relative term. A professional football player making 1 million a year is poor compared to Elon Musk. This is why you have to standardize your terms. If you stated that poor was those without housing, stable food sources and basic water, electricity and hygiene systems then you will suddenly find that the US has very little poor in it (hard to get this exact number, but it's smaller than 5%). If you make poor defined as those who have less than 1/1000th of the top income earner then you will find out that 98% of the US is poor.

[@MJAY-N7129]

This channel is such a delight! I have always enjoyed math but since my teachers in high school weren't the best, I gradually lost interest in it. These videos have definitely reignited my interest in math. Thank you so much for sharing this!!

[@ruthgentle9622]

I am preparing for a teacher certification test in another state and this video was very helpful and easy to understand. Thank-You!

[@GallantryX]

This is amazing, I really like this video so much, when you don't understand a particular part in Statistics, and expect typical whiteboard and boring learning, you find this amazing video that makes you even enjoy learning, thanks!

[@kibrika]

A great moment of serendipity has occurred! I was taught in school some 20 years ago or so a cool way to make patterns out of knots. I kinda wanted to relearn how to do it, but couldn't figure it out or easily find it. Thank you for mentioning macrame to me!

[@tomasgd93]

Extraordinary explanation! I just shared the video with my coworkers

[@4Goalkeepers]

You make people that wouldnt search for subjects like statistics, actually watch and learn statistics, because you make it clear, and fun! Thank you. I will recommend you all over :)

[@jessemounts9209]

Thank you crash course! This really helped me grasp these concepts.

[@gah-kaileung7075]

I wish my university stats classes were as fun as these videos.

[@sidzilpe9391]

Ok . Now I understand..... CRASH COURSE IS SLOWLY MOVING FORWARD TO CRASH COURSE MATHEMATICS.

[@melonlord1414]

Mathematics is too broad for one series so they probably split it into multiple courses. Statistics is just really fitting right now while the social science course is nearing it's end.

[@levi12howell]

I loved the admission that accurate statistics can be misleading. The mean vs median ncome example was perfect

[@babebave]

THANK YOU SO MUCH!!! I love this!!! So much better than re-reading the same sentence in my textbook. Can you make one for Z-Scores and Standard Deviation?

[@crazymorena801]

I LOVE STATS!! It was my favorite class in college. Thanks for your videos! 🎉🎉

[@murphygreen8484]

This has been my favorite crash course yet. Thank you!

[@flynjack4304]

Man i'm gonna need to watch this more than once.

[@_ten_10]

Thank you for this series! It's been of great help to me.

[@Reverserandy]

"There are three kinds of lies: lies, damned lies, and statistics."

[@xcbu10x]

-Mark Twain

[@danford570]

Many thanks from a humble psych teacher for the clarity!

[@isabelbraico7178]

tfw u start studying for ur ap test 13 hours before it starts... thanks crash course! love u

[@hem89180]

I just love these guys!!! Keep up the good work!!

[@pantheraigni]

Wonderful, exactly when i start to utilize R. thanks

[@simpplyari]

This is what I’ve been waiting for!!! Ugh Thank god for this video 😭

[@alyssayoung5994]

Here again, for I want to tell you thanks for saving me throughout college. Especially Statistics!!!!!!

[@Ronenlahat]

Amazing host! Do Crash Course distributed computing & byzantine fault tolerance!

[@allisonphillips1682]

Loved this class thanks for teaching me!

[@israel.horowitz]

Such Clarity! Thank You so Much!!

[@meireleshotmail]

Loving this!! Better than any other math class

[@robspiess]

I had no idea my pie with ice cream on top was so fashionable.

[@claushelge1366]

You're great, Adriene.

[@danawall1785]

My favorite channel on KZbin!

[@marykatebailey8308]

Just did this in Stats class! Your videos explain the course material enough for me to follow along, and for that I thank you!

[@cartonofjaws6116]

This was cool. It's not hard to understand what the difference between these three are but no one's ever explained to me how the relationships between them can be useful

[@nickrobinson1648]

Thank you for these videos.

[@abdelrahmanashraf7636]

Although the whole series is great, this video was ultra extremely great

[@FNButterStrings]

This course is a great supplement to the computer science course.

[@chingsangmawimunsong9526]

Thank you so much for this free tutor.

[@NeufeldIan]

There have been a few comments about "you can totally make an average color" and I would like to address some of that. Because I think colors and vision are interesting and I'd love people to have a better understanding of both color and statistics. The first obvious suggestion is that the visible spectrum is composed of wavelengths of light. You probably know that visible light spans a wide range of colors from looking at a rainbow that splits up the many different wavelengths (ROYGBIV). Obviously if someone picks "red" or "blue" you can point to a place in the visible spectrum where the light is red or blue and assign their color a wavelength, right? Well ... white isn't part of the rainbow. There is no single wavelength that corresponds to white. White is a mix of many wavelengths of light which our brain interprets as white. And black is of course the absence of light, so there's no wavelength to assign it. Worse, it turns out that if you get more specific in terms of your favorite color (not "red" but "crimson", not "blue" but "cerulean") then that exact color is probably not single wavelength but rather a combination of many wavelengths. For the sake of argument though, let's add up all the values we can represent (ignoring white, black, grey, brown, pink, gold, silver, etc etc) and we will *absolutely* get the average color as some shade of green, barring some really intense skew in people's favorite colors. Green is in the mid range of the visible light spectrum and unless an absolutely massive proportion of the people favor blue/purple or red/orange, the average will be green. The exact shade of green will vary depending on whether or not you do some fiddling to make the visible spectrum more "even" than it actually is. The second suggestion is that our computers model color for us through Red, Green, and Blue light. This is a cool trick based on the fact that we don't individually detect specific wavelengths. Our eyes are composed of three types of color receptors (cones) which are each most active in a certain part of the visible spectrum. These cones report back their activation levels and from that our brain constructs a perceived color based on how much each of the cones in a particular particular part of the eye are active. There's even a cool trick that because our Red cones are slightly active in the violet-end of the visible spectrum we can combine Blue and Red light to create Purple! That's really cool and allows us to smoothly transition from violet back to red by reducing the amount of blue light even though those points are on opposite ends of the visible light spectrum and a direct wavelength transition between those values should require us to pass through green. Instead we perceive those two ends as linked - almost like the visible spectrum is a "color wheel". Now, even though RGB does not allow us to encode every visible color, it does give us a more nuanced system for capturing colors that involve multiple wavelengths at once - or even no wavelength! We can capture white, black, grey, brown, and many other colors that aren't handled by a single wavelength. We can also capture the same wavelength at multiple levels of brightness so we can distinguish someone who likes "light red" from someone who likes "dark red". If we build RGB representations of each of their favorite colors and average out those RGB values, we can calculate an average value and it will be some shade of grey, possibly with a hint of one of the three channels being higher or lower than the others. Because roughly equal amounts of Red, Green, and Blue light will make some shade of grey. A variant on this suggestion though is that when we print we use a different color model. Instead of RGB (which is based on adding light together), most printers use the CMYK model (which is based on mixing inks that subtract light from a piece of white paper). Using Cyan, Magenta, Yellow, and blacK, we represent all our colors using 4 values, mix them together, print out the average and get brown. Because when you mix roughly equal amounts of Cyan, Magenta, and Yellow you get a brownish color, then darkened by however much blacK gets used. I'd like to pause and take a moment to think about what happens when we calculate averages in other places in statistics. If we calculate everyone's height in inches and take the average, then switch to centimeters and take the average ... we'll get the same answer. If we calculate average people's age in years, then do it in minutes, we'll end up with (minus some rounding problems) the same answer. If we average everyone's income in USD, then convert it to Euros and average it ... we'll end up with the same answer. But here we've taken three different ways of measuring and representing colors, averaged the inputs in each of them, and gotten wildly different results. No one would mistake green, grey, and brown as being the same colors, so something weird is happening here. Let's try one last thing in hopes that we can resolve this. Rather than resorting to CMYK or RGB systems which are outputting in a limited number of channels, let's go one step further. We ask everyone to bring in an object they own that is their favorite color. Then we'll point a light sensor at it and measure ALL the wavelengths coming off the object, average how much of each wavelength is coming off the objects in question, and then we'll have our absolutely accurate answer. Your assistant shows up carrying two purple objects and says "both of these are my favorite color, but I couldn't decide which one to bring, so let's measure both of them and take their average." You agree and measure the light coming off one of them, then the light coming off the other ... and then hang your head in defeat. The two objects have very different sets of wavelengths being measured, yet your eyes consider them indistinguishable. Where one of the two purple objects is mostly reflecting violet light, the other's color appears to have been made by mixing blue and red paint so it reflects very little violet light and much more red and blue. Showing your assistant the average of the two brings a shake of the head, "that's still purple, but it doesn't look like either of them!" In fact, there could be hundreds or thousands of combinations of wavelengths that all map to this same shade of purple, because just as our computer shows millions of shades using only 3 wavelengths, the natural world is reflecting hundreds of thousands of wavelengths that we only perceive as intensities in our 3 types of cones. In the end, we're left wondering why it's so hard to pick an average color - we have 4 systems that assign numbers to colors, but they give conflicting answers. This is an important distinction then between a numerical representation and a measurement. You can measure the number of pets in each household and determine the mean number of pets each person has - that's great. But if you assign a number to each of those types of animals (1 = dog, 2 = cat, 3 = goldfish, etc), you've created a numerical representation of a qualitative value. If you then average THOSE values, you do not end up with a meaningful result - especially since you could just change the values in your representation and get a different answer. Wavelengths of light are interpreted by our brains as colors, and while wavelengths are a physical phenomenon you can measure, "color" is not a one-to-one measurement of the physical world.

[@aaronmarks9366]

This was a fantastic post. Thank you for taking the time to write it..

[@inaradamji7514]

You explained it so well!

[@manwith6.9inchpenis72]

I predict that the next episode will be about Measures of Dispersion

[@vampyricon7026]

Good job!

[@manwith6.9inchpenis72]

Vampyricon Thanks!

[@yamenarhim9336]

the prophecy is true he is the chosen one !

[@jeralyncabaluna5819]

This is so helpful

[@dylanbh1]

this course is just in time to save my failing stats grade ;)

[@omarkhalaf7014]

This made me understand the concept rather than what books do, tell you how to calculate the central tendency values with vague explanations which then leads to memorizing and not thinking.

[@cosmicwarriorx1]

Finally after all these years i understand median and mode.

[@harichandana4799]

Some of the examples are taken from the book The Tiger that isn’t by Michael Blastland and Andrew Dilnot. Worth the read.

[@tania-ld5xo]

i love the refrences

[@MohamedEssam-fd4en]

This is just great!!!

[@darem7034]

Thank you so much!

[@Aritul]

I love Crash Course. Thank you for these videos, all of them.

[@alanblitzer744]

Love u guys!

[@chillsahoy2640]

In A-level we were taught that "average" is an umbrella term for these three measures of central tendency: mean (which is what non-mathematicians normally intend when they say average), median and mode.

[@MiguelCruz-hh9vm]

This was coincidentally the subject of today's lecture in my biometry class

[@fatbasterd5195]

If only the news would present data like that...

[@ajgiliana]

You get 👍 just for the padres lineup you chose. Taking me back...

[@Shaunss]

Awaiting a video on chi square tests of GOF, homogeneity, and independence/association. I can't tell which test to use given a problem :/

[@aaronmarks9366]

Same

[@ricofficial2082]

Hi i really enjoy watching these courses, could you talk about bose einstein statistic?

[@rlee1231]

Thank you! 🥰

[@ChrisBigBad]

this is the third video, i watched to understand this topic. Thank god the others were short. and: does she sound like Bill Hammack The Science Guy?

[@inkkbell]

Question on Statistics: Can you do a correlation coefficient with more than two variables? I'm trying to if my data correlates between ages. Which formula would you suggest?

[@Byron3189]

please do more crash courses in other areas of math!!!

[@Eddn102]

I jump the freeway median, I'm savage Cause my mode is that I'm meaner than the average - George Watsky

[@yamenarhim9336]

Nice example i like it !

[@aaronmarks9366]

Watsky slays

[@jiensuyang3915]

love how teach !

[@gerardoixehuatl6776]

Interesting... A good way to do math videos

[@bentech9319]

This channel is such a delight! I have always enjoyed math but since my teachers in high school weren't the best, I gradually lost interest in it

[@jadedadiz9018]

How does this only have 158,000 views?

[@TheR971]

Elon musk playing with falcon heavy is soooo current and great!

[@SergioLongoni]

Also the flamethrower on the left :-)

[@TheyCalledMeT]

current? i thought we're at statistics not electical engineering

[@bazalbaz]

It landed.

[@spinningsouthafrica]

he from south africa

[@Tfin]

Sure there are mean and median favorite colors, as long as the colors involved exist within the spectrum of light (visible or otherwise). Each color on the spectrum is easily converted to a number, and math happens. Non-spectrum colors get a bit more involved.

[@estebansalami6274]

wow !!! , this is strangely giving me interest on Statistics.

[@TranslatorCarminum]

8:04 - 8:15 No such thing as an average favorite color? In the digital age, I wouldn't be too sure about that. You could theoretically find the mean R, mean G, and mean B value and composite those three components into a sort of "mean" favorite color. In a very simple example, Roy likes red (255, 0, 0), Bill likes blue (0, 0, 255), Greg likes green (0, 255, 0), Yolanda likes yellow (255, 255, 0), and Pete likes purple (255, 0, 255). This would make the "mean" a color of about (153, 102, 102), which I believe would be a dull reddish tone. Just a bit of fun!

[@vainbow4632]

And now you've ended up with a color that neither Roy, Bill, Greg, Yolanda nor Pete like lol

[@hawzhinblanca]

very useful

[@Desi-qw9fc]

Geometric or harmonic mean can also be used to give outliers less weight.

[@paolobarazon]

2:35 the bell shape graph is on the left but she's pointing at the right side of the video 😂

[@cortanad.3589]

Hope we can finish this by having the AP test in May

[@moustafamohsen]

" *But we all gotta use our common sense* " - Like for being a median scientist

[@tenou213]

Crash Course stats? YES

[@intheshell35ify]

Once again crash course saves my bacon.

[@Danilego]

This reminded me of that one Cookie Clicker news joke, that said "the average person bakes 8 octillion cookies" or something(because the player is an extreme outlier), I think they could use a Median in this one!

[@Kalaphant]

0:38 I was about to say 2, when I caught myself lol

[@xsaberfaye]

Anyone else notice Michael Lewis' Moneyball on the left in the background?

[@sarahmarshall7523]

I found the "speed" of talking & information given for "learning" about some of this was so fast it was to "fast". I left like she was just trying to go over information she was super familiar with for so long, with others in that similar category of the relation to "her" knowledge on this subject.... "Slow it down some so we can remember this stuff well". ;)

[@sherrychen710]

I hate stats and I never expected AP Psych to bring me here...

[@lorenzomontenegro4313]

This should be shown to classrooms! Great way of educating Statistics.

[@Starcrash6984]

I'm glad you specified that by "average" number of feet you meant "mean", though you're still equivocating a bit when you use "average" to describe what most people interpret as "typical". Median and modes are "averages", too, and both of those for the number of feet of a person has gives you an "average" of exactly 2.

[@flaviusclaudius7510]

She also didn't state what _type_ of mean; she describes the arithmetic mean, but the geometric mean or harmonic means would both give different answers (both less than two, though).

[@coolwhoami]

A useful exercise (and icebreaker) I used when teaching measures of central tendency was to have this very discussion about the use of the word average in everyday language, and its detachment from arithmetic means. An important concept to be clear about!

[@KatrinaEames]

How do we ask good questions about the statistics that we see?

[@jacobsim3971]

This was just repeating what I learnt in primary school math

[@anastasiaradionov]

Wow, this was the only time someone made statistics sound interesting.

[@jeralyncabaluna5819]

Will you make a video about ANOVA?

[@aaronmarks9366]

I hear PBS has a series on that.

[@cuzco08]

Is there no way to accurately count large numbers? Or is guessing still our best option?

[@BecksWood51]

Is anyone hearing in the background Timmy Tim singing "statistics, statistics.."? oh right, it's just me lol

[@robertgarcia2689]

thanks

[@thajayplaysmobile1739]

I love statistics