Central limit theorem | Inferential statistics | Probability and Statistics | Khan Academy
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- Опубліковано 25 січ 2010
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Introduction to the central limit theorem and the sampling distribution of the mean
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Why can't teachers explain things this clearly, why do they have to act all scholarly?
because they don't understand it either!
did u watch the next few lessons?
because they are scholars, not pragmatist, like you !
Well I think what's mostly going on is that there are different levels of understanding for a topic. Sometimes, if the explanation is not clear it's because the instructor is making room for some of the subtleties down the line. For example, imagine how confusing Newtonian mechanics would be if instructors always fixed the tiny error due to relativity. Or, like someone said below--maybe they don't have a clear understanding yet.
a true mastery means that one can teach it simply and clearly
Honestly, this almost 10 minute video helped me understand something we were learning in class for like 2 weeks! Thank you so much!
that two weeks of study is the reason you can enjoy this clip so much.
@crni195 Like a true engineer you had to point out that you are one lol
Superb Khan sir, am very pleased to study statistics as I watched your 10 minutes videos
are you alive ?
Very, very cool stuff. Also, you're obviously a smart guy, Sal. But at the same time, you're incredibly accommodating to us students. Thank you for your sincerity and empathy, sir.
cramming for my stats exam tomorrow
Cramming for my stats final today
same except in 20 minutes
Me rn
Not cramming. :P trying to learn it as much as possible.
@@CrunchyDark big flex
Drinking game: drink whenever you hear the word "sample"
i6mi6 I might need to play that game to get over my probability score... D;
no
lets just kill braincells before the exam..
Are you intoxicating that I'm insinuated?
I'm trying to study here shhh
These videos have been tremendously helpful! Thank you SO MUCH for making them! The concepts make so much more sense when I can see them being worked out.
You explain this better than a textbook. You are a great!
Fantastic explanation. A shame that most teachers are not educated enough to be able to understand and explain things like this to their students.
so true
...and when they are educated, they start believing it's super obvious so they just tell you what it is without examples and in depth explanations and jump straight to the following topic, expecting you to have not only understood but also interiorized the concept.
@@mrknarf4438 This so much. I love when they have 200 students in front of them and when the teacher asks for an answer to a question and nobody answer it's everyone else's fault. They never think maybe it's their fault they suck at teaching. Sal is amazing, I only wish topics were more in depth.
Dear Sal. I always skip all my calculus and statistics lectures and come straight to your videos. This has been the secret to my success in university. Thank you!
you are amazing , thank you , not only for this video , but for all your videos that i have been using for 3 years :)
This video summed up in almost 10 minutes what I have been trying to understand in my textbook for the past week. Good stuff...thank you!
I have been a mathematician all my life. I dropped out after middle school but started to get bored, so I bought some mathematics books with the answers at the back and used them to self-study for university entrance in the UK. That was 50 years ago before I graduated with scholarships for Oxbridge after gaining a double first-class in pure mathematics and theoretical computing. With hindsight, I feel your videos would have been really useful for statistics which I dropped for pure mathematics, applied mathematics, and physics. You are always highly recommended to all my tutees struggling with their education during this pandemic. Excellent material!
Thank you! Thank you so much! Thank you very much! I have been in Intro to Econometric class for 2 months already. I feel I understand more from your video for 10 minutes than in class for 2 months
I was given 3 20 minute videos on this subject and I didn't understand a thing they were trying to tell me, but I watch one 10 minute video from you here, and I completely understand this now. Thank you so much, KA.
You are helping me get through my graduate level quantitative analysis classes. Thank you so much ! =)
Heck yeah, this is a great motivating video... gives an outline of the idea and why it's so cool and important!
This video was posted 10 Years ago and still so useful!
Such a crazy thing
So cool. I took Stats 101 about nine years ago, and these videos were there for me. I'm back in grad school now, and you're videos are helping me with Applied Stats once again. You rock!
Can u explain me in somewhere.... actually I didn't get what is related to central limit theorem. Is it Sample size or no. Of samples from which we calculate mean.
went to lecture today and read the chapter and was clueless. I watched the first 7 minutes of this and the concept is crystal clear!!
you guys are shaping history. thank you.
I mean this is brilliant! Got me thinking and understanding deeply.
may god bless you Sal!!
You are my guru
you are the voice in my head as i solve math
Best explanation out there. Thanks, Sal!
Nothing much to say how good you are, the video tells it all, keep up the good job!!!
I'd like to really thank you for your videos. All of them with great didatics and only now made some aspects of statistics very clear for me :)
You just made life so much more interesting. Love you Sal! Will donate soon.
You just saved my life brv.....you explained in 9 minutes and 49 seconds ,what ive been trying to understand for the last 2 hours.
I like it that it's called Khan Academy. KHAAAAAAN!!
Thank you for your clear explanation. You are a world class educator!
This channel is a life saver!
khan is awesome ! Im in this course that could not explain this well. I need to know the principle and Khan blew it out of the water ! I know the principle and the APPLICATION ! sweet
Thanks! Got a test that includes this section next week and it had me stumped
If x = 1,3,4 or 6 and the sample size is 4, there would be 4*4*4*4 possibilities i.e. 4^4 possibilities =a maximum of 256 possible outcomes so by taking 10,000 samples you will be repeating each 1 about 40 times.
Henna George yes, and if you take an infinite amount of samples, the distribution of the sample means will show the probability of getting each sample.
THANK YOU!! Your videos are amazing, such an amazing and intelligent man!
my teacher just mentioned the central limit theorem and did not explain it (in 1 week!) :D and I just spent 10 mins to watch this clip to understand what he tried to explain in 1 week (and no one understand) :D thank you so much!
It's been 13 years since upload and people like me are still using these videos... Great explanation!
I love you man
it's a lot of fun learning this stuff.
Thanks a lot
I never took a stats class in high school or college and the bootcamp class I am currently taking does not do a good job at explaining this theorem. So who do I turn to? Sal! I grew up with you and you are still helping me learn even in my near thirties. Thank you!!!!
Very instructive video!
Done thanks
4:30 looking at the SAMPLE MEANS (taking a sample of n measurements, then averaging those n measurements is the sample mean), doing this for x samples of n measurements we have x sample means
The distribution of these sample means tend towards a normal distribution as we take more samples. Also as the sample size the number of measurements in each sample increases, the sample means distribution approximates normal even more
A good way to explain CLT. From an unknown discrete distribution to converge to a normal distribution.
Oh man, that is SO logical!
helped me to pass my statistic class. thank you!
Thank you very much for this very clear explanation!
Much better explanation than my textbook, thank you so much
Once again Khan Academy saved me from the state of I am not able to understand to how easy is this stuff. Thanks
"1" is one element of the sample, so is another "1", as well as "3" and "6", therefore there are 4 total elements that comprise the whole sample, thus the sample size, n, is equal to 4. It's 4 in this case because that is the sample size this person decided to use for his test. Higher sample sizes usually lead to more accurate tests.
If I say "What is the sample size of all possible outcomes on rolling a die?", there would be 1, 2, 3, 4, 5 and 6, meaning n=6.
Thank you for this explanation. I would like to ask you a question. If we got a distribution (probably heavy tailed) and take many samples with different size (for example the first sample will have 30 samples, the second 40, the third 34, the fourth 51 and so on) will then the distribution of those samples be normal?
The video is simply beyond cool. Thank you so much sir.
thanksss, i loved your video, i was looking to prove CLT and it clarified niceee
Your video is easy to understand. Thank you^^
thanks. This is way more straight forward than the aihl textbook
Very clear. Thank you
OMG!!!u r much better then my lecturer!!! He talks like a computer n I can just keep copying the solution of the examples during the class!!!!
I understand much better becoz of u!!!!!!thx a lot!!!!!!!!!!!
Thank you so much for a clear explanation.
Very helpful! thank you so much, Sir!
YOU ARE SO AMAZING. PLEASE KEEP DOING WHAT YOU'RE DOING.
I need to pass my exams...
have you passed?
Great explanation!!
Thanks for the explanation!
God bless you ! I got this after 10 years...
This is extremely well explained ! Thank you teacher.
damn this is actually really cool
You can use the word "observations" for the elements in a sample.
Thank you for very nice and instructive Probability series. I would like to see mathematical analysis of random walks - will you create it?
Thankyu so so much!!!!!
This was a very useful video. Thank you so much. Clear and interesting explanation. Although the "peak" of the normal distribution should be around 3.5 in your example, not 2.75. Since that's the mean. Right?
I love statistics!
awesome video!!
Very Good example ... I was having problems with figuring out how the individual mean element was obtained...
You, sir, are The Real MVP!
who's out here cramming for the ap stat exam thursday
great xplanations sir...thanks so much...
you nailed it. thanx a lot
Jeez, thanks for driving it home! You need to get with a publisher and go wide, you explain in the most basic, and common fundamental way for easy learning.
You have a great channel. I am in a master's degree program, and I still use your site.
Beautiful. Made my day.
I heard about the elegance of math: think I just got it!
Thank u so very much u helped me a lot
Thanks Sal !
As the sample size (i.e "n") increases the sample distribution starts looking more and more like the normal distribution. Does it have to do with also the number of samples taken? If I were to take 10000 or 100 sample of the same sample size (n) then would both have the normal distribution? Thanks!
Khan is getting me through college
Sal.... Your my rockstar!
Your welcome
Very nice explanation. Hats off.
THANK YOU!!!
Central limit theorem = mind blown
thank u, so helpfull!
Thanks so much !
it's really helpful
It is good to know that your brain malfunctions from time to time, too lol Thanks for the great videos!!!
great work..
Fantastic!
great vid!
You are just awesome..!
U r helping me a lot :D
thank you!
this man khan do anything
The U-looking symbol you're talking about is the greek letter μ or Mu. It represents the mean. In this video, he used an x-bar (just an x with a bar above) to represent the mean because it is was specifically for a SAMPLE. In other words, you use μ for a population mean and use x-bar for a sample population.
It's sad how many people commented here saying that their teacher could not explain it. It seems most teachers are not good at their jobs. Where in the world would we be if we didn't have contents like Khan Academy?? Thanks to the internet. Thanks to people like Sal
This was beautiful
i've figured him out... He went to a good school and learned this beginner subjects and mastered them because of good teachers, and then he words it into a 10 min video and impresses all of us...