Mean, Median, and Mode: Measures of Central Tendency: Crash Course Statistics #3
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- 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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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.
Oh god I'm watching for fun a class that I hated
Lucio Fernandes same here hahahhaha
the end of school as we knew it
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
im taking statistics next year so im glad this is coming out now
Lucio Fernandes same
The fact that crash course is free is such a blessing
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 :)
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!!
I predict that the next episode will be about Measures of Dispersion
Good job!
Vampyricon Thanks!
the prophecy is true he is the chosen one !
My favorite channel on TH-cam!
tfw u start studying for ur ap test 13 hours before it starts... thanks crash course! love u
You're great, Adriene.
This course is a great supplement to the computer science course.
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!
I LOVE STATS!! It was my favorite class in college. Thanks for your videos! 🎉🎉
Extraordinary explanation! I just shared the video with my coworkers
If only the news would present data like that...
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?
How does this only have 158,000 views?
I jump the freeway median, I'm savage
Cause my mode is that I'm meaner than the average
- George Watsky
Nice example i like it !
Watsky slays
Some of the examples are taken from the book The Tiger that isn’t by Michael Blastland and Andrew Dilnot. Worth the read.
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!
And now you've ended up with a color that neither Roy, Bill, Greg, Yolanda nor Pete like lol
Finally after all these years i understand median and mode.
Elon musk playing with falcon heavy is soooo current and great!
Also the flamethrower on the left :-)
current? i thought we're at statistics not electical engineering
It landed.
he from south africa
Awaiting a video on chi square tests of GOF, homogeneity, and independence/association. I can't tell which test to use given a problem :/
Same
This is what I’ve been waiting for!!! Ugh Thank god for this video 😭
I hate stats and I never expected AP Psych to bring me here...
Interesting... A good way to do math videos
Love u guys!
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?
Will you make a video about ANOVA?
I hear PBS has a series on that.
This was coincidentally the subject of today's lecture in my biometry class
I love statistics
There are two pieces of bread. You eat both. I eat none. Average consumption: a piece of bread per person. -Nicanor Parra.
Crash Course stats? YES
Once again crash course saves my bacon.
Anyone else notice Michael Lewis' Moneyball on the left in the background?
Thank you! 🥰
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!
This is so helpful
Thank you for these videos.
wow !!! , this is strangely giving me interest on Statistics.
2:55-3:13 wouldn't mode be your best guess in that situation? That is the most frequent number in the data set and therefore most likely to be an individual data point.
For instance the foot example said the average person has less than one foot. Let's assign it's value as 1.7 for this situation. If I had 5 friends online, and i were to try guessing how many feet they have; 2 would be a better answer than 1.7 . I know this particularly works in the example since you only have 3 options (0,1,2); but that makes mode the best option since it indicates the most frequent answer. Median isn't necessarily a data point in the set, since when it's an even number you usually average the two to get median (meaning that value:IS NOT part of the set). This displays that Mean and Median aren't even necessarily equivalent to a data point in a set.
Question: If there is only one value for mode; is that always going to be the best metric for guessing someones data point from a set?
love how teach !
Is there no way to accurately count large numbers? Or is guessing still our best option?
please do more crash courses in other areas of math!!!
Hi i really enjoy watching these courses, could you talk about bose einstein statistic?
Is anyone hearing in the background Timmy Tim singing "statistics, statistics.."? oh right, it's just me lol
This is just great!!!
I always thought a la mode meant with ice cream...is ice cream fashionable? I'm probably crazy lol
omg, are you the voice behind Amoeba Sisters'?
don't forget the existence of non-parametric aka ordinal data and how median is its center
Your background is "normal" and cool at the same time.
Is it possible to describe 'mean' time since time in this context is not quantitative data?
...normal is only local, except for infinite sample sets... multimode has more information... averagings, numbers-of-puppies-per-litter, assume all source-sets have the same mode of operation, but that, is information, first, not statistics first-so, when do you do statistics...
Yeah!!!
Despacito popular! 😂 Love her!
2:39 pointing in the wrong direction thats ok but funny
Please do correlations
4:43. meow, meow, me. ohhh!
I'm falling in love with Adrian!
this lady do be looking like my teacher tho...
am i the only weirdo that goes to in-n-out at 10 am, lol
I mean it
Okey, but how do we calculate the modes?
Statistics gets complaints that the measurement system last episode was too limiting. So they respond with In-n-Out.
Maybe I DO have a half cat, you don't know my life!!!
"Like Despacito popular" hahahaha
Or in Great Britain three
?
Two And A Half Cats, I watch that.
But most people have 2 feet so how is that more than average?
LegendofVII ...watch the first minute again with the sound or caption on
4:14 I don't get this?! Shouldn't the median be 3?
Edit: Ohhh the hell? I thought she was talking about the number of cats. I wish this was phrased better.
Butbutbutbut... Blue is my favourite number of the alphabet; surely you can find the average...
mmmm, In and Out :P
The way she explains needs to be more in a simple way
You don't need to deceive you just should obfuscate them (statistics) :(
ANIMAL SAUCE BURGERS AND FRIESSSSSSSSS
I'm disappointed that you did not share your own views on pineapples on pizza.
Average favorite color? You can totally just average the RGB values
Wouldn't there actually be an average favourite colour though?
Not in the sense of "mean", no.
I can think of ways to derive one - since there are numbers behind colors, whether they're wavelengths of light or rgb/cmyk values.
AlthenaLuna No single wavelength of light represents a colour like “white” and neither RGB nor CMYK fully encompass the human vision space.
If you wanna get super pedantic and condescending, maybe. If astronomers are willing to give an average color of space - cosmic latte - I'm pretty sure we can get a reasonably close representation of an average favorite color.
AlthenaLuna The problem is that there’s an important distinction between emission and absorption. A star emits a clear amount of each wavelength. Our eyes, however, do not perceive each wavelength or combination thereof uniquely. That’s how a computer can use Red/Green/Blue light to create the illusion of yellow or purple.
We could show people pictures of objects on a computer and use the R/G/B values of the pixels we may get a very different answer than if we ask them to point at objects and measure the light coming from there. There ma be hundreds of different combinations of light that result in people experiencing the same colour.
I'm above average!!!! I have 2 legs!!!
me to i have 20
Statistics has it's moments. The mean is one of them.
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.
thatisjustgreat I don't know, the mean is kinda average
+
The first one in my opinion
"As soon as Musk walks into the room, the average income skyrockets", I see what you did there..
"There are three kinds of lies: lies, damned lies, and statistics."
-Mark Twain
Ok . Now I understand.....
CRASH COURSE IS SLOWLY MOVING FORWARD TO CRASH COURSE MATHEMATICS.
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.
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.
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.
Pfhorrest this
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.
Speak for yourself! *eloquently sips cup of tea*
average =mean . how do you group? I mean what are the bin sizes?
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.
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!
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!"
I had no idea my pie with ice cream on top was so fashionable.
I wish my university stats classes were as fun as these videos.
Wow, this was the only time someone made statistics sound interesting.
Very useful analogies - Adrienne is doing a great job so far!
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!
Man i'm gonna need to watch this more than once.
" *But we all gotta use our common sense* " - Like for being a median scientist
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.
This was a fantastic post. Thank you for taking the time to write it..
the examples given are too confusing
this course is just in time to save my failing stats grade ;)
Pretty sure someone could figure out the avarage colour by rgb values but i could be completely wrong
That would be a way of finding the average, but is it more legitimate than finding the average in CMY colourspace? The central values for whose green colour receptors corresponds with the 'G'? What about tetrachromats? What about colours that exist outside of RGB colourspace? There are lots of ways you could define 'mean colour', so the concept of 'mean colour' itself is pretty vague and meaningless.
Or the wavelength average
I loved the admission that accurate statistics can be misleading. The mean vs median ncome example was perfect
It silly how she went from cats because of the 2.5 cats average to macrame knots. Guess averaging 2.5 cats isn't a fun visual aide. But the cats were so cute!
Of course you can have 2 and 1/2 cats: Schrodinger proved it with the through superposition with his cat being both alive and dead.