Central limit theorem | Inferential statistics | Probability and Statistics | Khan Academy

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  • เผยแพร่เมื่อ 3 ธ.ค. 2024

ความคิดเห็น • 340

  • @gopikarajanikanth4482
    @gopikarajanikanth4482 10 ปีที่แล้ว +334

    Honestly, this almost 10 minute video helped me understand something we were learning in class for like 2 weeks! Thank you so much!

    • @johnanderson8765
      @johnanderson8765 5 ปีที่แล้ว +4

      that two weeks of study is the reason you can enjoy this clip so much.

    • @aniruddha4672
      @aniruddha4672 4 ปีที่แล้ว +8

      @crni195 Like a true engineer you had to point out that you are one lol

    • @natureloving785
      @natureloving785 3 ปีที่แล้ว

      Superb Khan sir, am very pleased to study statistics as I watched your 10 minutes videos

    • @shakuntalakamade
      @shakuntalakamade ปีที่แล้ว

      are you alive ?

  • @matthewwroblewski8752
    @matthewwroblewski8752 8 ปีที่แล้ว +319

    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.

  • @SuperYtc1
    @SuperYtc1 7 ปีที่แล้ว +81

    Fantastic explanation. A shame that most teachers are not educated enough to be able to understand and explain things like this to their students.

    • @sophiefeng2740
      @sophiefeng2740 5 ปีที่แล้ว +2

      so true

    • @mrknarf4438
      @mrknarf4438 4 ปีที่แล้ว +18

      ...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.

    • @Saiphel
      @Saiphel 4 ปีที่แล้ว +7

      @@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.

  • @esmeralda4884
    @esmeralda4884 8 ปีที่แล้ว +54

    You explain this better than a textbook. You are a great!

  • @jasminespence6452
    @jasminespence6452 4 ปีที่แล้ว +30

    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!

  • @mimireyes04
    @mimireyes04 7 ปีที่แล้ว +234

    cramming for my stats exam tomorrow

    • @EmberArcher
      @EmberArcher 5 ปีที่แล้ว +14

      Cramming for my stats final today

    • @carterwest9504
      @carterwest9504 5 ปีที่แล้ว +22

      same except in 20 minutes

    • @swatibiswas6796
      @swatibiswas6796 5 ปีที่แล้ว +1

      Me rn

    • @CrunchyDark
      @CrunchyDark 4 ปีที่แล้ว +4

      Not cramming. :P trying to learn it as much as possible.

    • @thesevenkg
      @thesevenkg 4 ปีที่แล้ว +5

      @@CrunchyDark big flex

  • @adamromero
    @adamromero 11 ปีที่แล้ว +481

    Why can't teachers explain things this clearly, why do they have to act all scholarly?

    • @deepakrp
      @deepakrp 4 ปีที่แล้ว +90

      because they don't understand it either!

    • @alenjose3903
      @alenjose3903 4 ปีที่แล้ว +1

      did u watch the next few lessons?

    • @yuningliu6300
      @yuningliu6300 4 ปีที่แล้ว +5

      because they are scholars, not pragmatist, like you !

    • @glennhenshaw7474
      @glennhenshaw7474 4 ปีที่แล้ว +4

      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.

    • @blakeelzinga1168
      @blakeelzinga1168 3 ปีที่แล้ว +18

      a true mastery means that one can teach it simply and clearly

  • @meganmaloney192
    @meganmaloney192 9 ปีที่แล้ว +44

    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.

  • @RachelLovelace
    @RachelLovelace 2 ปีที่แล้ว +8

    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!

    • @soumyaranjandas7394
      @soumyaranjandas7394 ปีที่แล้ว

      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.

  • @i6mi6
    @i6mi6 8 ปีที่แล้ว +660

    Drinking game: drink whenever you hear the word "sample"

    • @TeeNanners
      @TeeNanners 7 ปีที่แล้ว +13

      i6mi6 I might need to play that game to get over my probability score... D;

    • @rogersyversen3633
      @rogersyversen3633 6 ปีที่แล้ว +1

      no

    • @nellyaviles9342
      @nellyaviles9342 6 ปีที่แล้ว +9

      lets just kill braincells before the exam..

    • @samdavepollard
      @samdavepollard 6 ปีที่แล้ว +14

      Are you intoxicating that I'm insinuated?

    • @skyepaul261
      @skyepaul261 6 ปีที่แล้ว +10

      I'm trying to study here shhh

  • @BboyFadi
    @BboyFadi 9 ปีที่แล้ว +17

    you are amazing , thank you , not only for this video , but for all your videos that i have been using for 3 years :)

  • @Bella_Noches_
    @Bella_Noches_ 3 ปีที่แล้ว +3

    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!

  • @bluesky-mi2sx
    @bluesky-mi2sx 4 ปีที่แล้ว +3

    This video was posted 10 Years ago and still so useful!
    Such a crazy thing

  • @stelun56
    @stelun56 3 ปีที่แล้ว +5

    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!

  • @hxh2025
    @hxh2025 5 ปีที่แล้ว +2

    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

  • @kwsatl6066
    @kwsatl6066 9 ปีที่แล้ว +1

    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!!

  • @8dannygirl
    @8dannygirl 12 ปีที่แล้ว

    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.

  • @hou950
    @hou950 4 ปีที่แล้ว +6

    You are helping me get through my graduate level quantitative analysis classes. Thank you so much ! =)

  • @mostinho7
    @mostinho7 4 ปีที่แล้ว +1

    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

  • @thuuyenphamnguyen8899
    @thuuyenphamnguyen8899 4 ปีที่แล้ว

    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!

  • @Wooktent
    @Wooktent 4 ปีที่แล้ว

    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.

  • @hennageorge3259
    @hennageorge3259 8 ปีที่แล้ว +7

    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.

    • @noahschuler6388
      @noahschuler6388 5 ปีที่แล้ว

      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.

  • @pratibhas2468
    @pratibhas2468 ปีที่แล้ว +1

    It's been 13 years since upload and people like me are still using these videos... Great explanation!

  • @nazifataha8868
    @nazifataha8868 4 ปีที่แล้ว +1

    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

  • @SuperTurkeyKing
    @SuperTurkeyKing 12 ปีที่แล้ว

    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!!!!!!!!!!!

  • @kristennwang
    @kristennwang 2 ปีที่แล้ว

    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!!!!

  • @18gshock
    @18gshock 13 ปีที่แล้ว +1

    Nothing much to say how good you are, the video tells it all, keep up the good job!!!

  • @ChitimachanPanda
    @ChitimachanPanda 11 ปีที่แล้ว +2

    "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.

  • @TheSevenofMine
    @TheSevenofMine 9 ปีที่แล้ว +5

    I like it that it's called Khan Academy. KHAAAAAAN!!

  • @rodrigomorgado5524
    @rodrigomorgado5524 4 ปีที่แล้ว +1

    A good way to explain CLT. From an unknown discrete distribution to converge to a normal distribution.

  • @MayankMehta-pr9eg
    @MayankMehta-pr9eg 8 หลายเดือนก่อน

    Once again Khan Academy saved me from the state of I am not able to understand to how easy is this stuff. Thanks

  • @lllBOLTlll
    @lllBOLTlll 13 ปีที่แล้ว

    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...

  • @obinnadaniel2001
    @obinnadaniel2001 8 ปีที่แล้ว +2

    I mean this is brilliant! Got me thinking and understanding deeply.

  • @LYLxd
    @LYLxd 13 ปีที่แล้ว +3

    YOU ARE SO AMAZING. PLEASE KEEP DOING WHAT YOU'RE DOING.
    I need to pass my exams...

  • @Abubakar-ht5ee
    @Abubakar-ht5ee 6 ปีที่แล้ว +2

    you guys are shaping history. thank you.

  • @That1KoreanGuy
    @That1KoreanGuy 11 ปีที่แล้ว +2

    This channel is a life saver!

  • @usharagunath23448
    @usharagunath23448 5 ปีที่แล้ว +1

    may god bless you Sal!!
    You are my guru
    you are the voice in my head as i solve math

  • @aprilhicks3474
    @aprilhicks3474 4 ปีที่แล้ว

    You just made life so much more interesting. Love you Sal! Will donate soon.

  • @solticpanzer
    @solticpanzer 12 ปีที่แล้ว +1

    This made understanding this theorem a lot easier.
    Also, that is a really bad 4.

  • @yitianxiao6650
    @yitianxiao6650 8 หลายเดือนก่อน

    thanks. This is way more straight forward than the aihl textbook

  • @goktugguvercin8069
    @goktugguvercin8069 6 ปีที่แล้ว +1

    You can use the word "observations" for the elements in a sample.

  • @serachrysanthemum9687
    @serachrysanthemum9687 8 ปีที่แล้ว +2

    Heck yeah, this is a great motivating video... gives an outline of the idea and why it's so cool and important!

  • @sinchumithun1
    @sinchumithun1 13 ปีที่แล้ว +1

    I think there is a flaw, the normal distribution is more and more approximated when we increase the number of trials. As we increase the sample size we get the variance goes down and in the limit we get a delta function around the mean, which is a consequence of law of large numbers.

  • @samadhashmi
    @samadhashmi 8 ปีที่แล้ว +1

    I love statistics!

  • @aj-tg
    @aj-tg 5 ปีที่แล้ว +1

    Thanks Sal !

  • @joed9229
    @joed9229 9 ปีที่แล้ว +2

    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

  • @jamesrobsonza7752
    @jamesrobsonza7752 4 ปีที่แล้ว

    Much better explanation than my textbook, thank you so much

  • @ylast3756
    @ylast3756 ปีที่แล้ว

    your explanation is more elegant than a 45 min lecture from a top40 US college.

  • @richaunfacey5447
    @richaunfacey5447 6 หลายเดือนก่อน

    You have a great channel. I am in a master's degree program, and I still use your site.

  • @mracuraon18s
    @mracuraon18s 12 ปีที่แล้ว

    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.

  • @ytkv
    @ytkv 8 ปีที่แล้ว +2

    Best explanation out there. Thanks, Sal!

  • @Zurh1994
    @Zurh1994 11 ปีที่แล้ว +3

    Central limit theorem = mind blown

  • @chopper84a
    @chopper84a 11 ปีที่แล้ว +4

    I heard about the elegance of math: think I just got it!

  • @winterfell14
    @winterfell14 11 ปีที่แล้ว +3

    Oh man, that is SO logical!

  • @lorrainepinon
    @lorrainepinon 11 ปีที่แล้ว

    helped me to pass my statistic class. thank you!

  • @WilliamJSSequeira
    @WilliamJSSequeira 7 ปีที่แล้ว

    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.

  • @purps45
    @purps45 13 ปีที่แล้ว +1

    Just remember, this only applies to finding the Mean or Sum. I've heard people try to claim the CLT means you can treat any PDF like a Normal Distribution if you take enough samples.

  • @ayonrab
    @ayonrab 13 ปีที่แล้ว

    God bless you ! I got this after 10 years...

  • @jordantan5023
    @jordantan5023 3 ปีที่แล้ว

    Very Good example ... I was having problems with figuring out how the individual mean element was obtained...

  • @tango2olo
    @tango2olo 12 ปีที่แล้ว

    Mr. Khan, you are a Prophet in the world of education.
    Please start making vedios on training the so called Teachers, on "How to Teach" a complicated stuff in a lucid manner! They all need salvation too. :-p

  • @khanabdulumarkhan6713
    @khanabdulumarkhan6713 29 วันที่ผ่านมา

    Clear explanation & better

  • @diencai1812
    @diencai1812 4 ปีที่แล้ว

    Thank you for your clear explanation. You are a world class educator!

  • @pianoforte17xx48
    @pianoforte17xx48 3 ปีที่แล้ว

    You can say "4 observations in Sample ..." . Eases understanding

  • @Lunaizle
    @Lunaizle 12 ปีที่แล้ว

    this man khan do anything

  • @檜皮猫
    @檜皮猫 5 ปีที่แล้ว +1

    So correct me if I'm wrong: The central limit theorem demonstrates how larger sample sizes and a larger number of samples will lead to a spread more similar to a normal distribution.

  • @Nizchul
    @Nizchul 11 ปีที่แล้ว +1

    You are changing the world!..... seriously!....

  • @LeahInTheRye
    @LeahInTheRye 11 ปีที่แล้ว

    Thanks! Got a test that includes this section next week and it had me stumped

  • @choppertalk8291
    @choppertalk8291 11 ปีที่แล้ว +1

    Very clear. Thank you

  • @matevarga1401
    @matevarga1401 5 ปีที่แล้ว +1

    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?

  • @shareef3743
    @shareef3743 8 ปีที่แล้ว +5

    damn this is actually really cool

  • @davidmbeckmann
    @davidmbeckmann 9 ปีที่แล้ว +1

    Very instructive video!

  • @pritivalecha3147
    @pritivalecha3147 2 ปีที่แล้ว

    thanksss, i loved your video, i was looking to prove CLT and it clarified niceee

  • @richenjoshi7054
    @richenjoshi7054 3 ปีที่แล้ว

    Thank god you mentioned "frequency distribution".

  • @ShroukAbdulshafy
    @ShroukAbdulshafy ปีที่แล้ว

    Very helpful! thank you so much, Sir!

  • @vishnuvardhan2608
    @vishnuvardhan2608 8 ปีที่แล้ว +5

    Sal.... Your my rockstar!

    • @versus13
      @versus13 7 ปีที่แล้ว +2

      Your welcome

  • @GirlGirlicious
    @GirlGirlicious 7 ปีที่แล้ว

    You, sir, are The Real MVP!

  • @69erthx1138
    @69erthx1138 14 ปีที่แล้ว

    The tails of the bell curve should represent low frequency mean samples, like those lacking sufficient permutation, e.g. [1,1,1,1]. Is this a correct assertion?

  • @lyndsays1373
    @lyndsays1373 5 ปีที่แล้ว +19

    who's out here cramming for the ap stat exam thursday

  • @andthatsallll
    @andthatsallll 12 ปีที่แล้ว

    I believe the symbol for mean is a U looking symbol... The one you did was for standard deviation
    ... either way you helped me out thanks

  • @valtih1978
    @valtih1978 11 ปีที่แล้ว

    Ok. Varying the sample size between 1 and ∞ we get the transit distribution between our original one and the normal distribution.

  • @flyingspur930
    @flyingspur930 13 ปีที่แล้ว

    you are much better than my professor

  • @Gold_Lagoon
    @Gold_Lagoon 5 ปีที่แล้ว

    this is gonna save my statistics grade

  • @guptaaniket274ag
    @guptaaniket274ag 2 ปีที่แล้ว

    Thankyu so so much!!!!!

  • @임상일-h7f
    @임상일-h7f 6 ปีที่แล้ว

    Your video is easy to understand. Thank you^^

  • @SamahGomaa
    @SamahGomaa 2 ปีที่แล้ว

    I am a big fan of khan Academy ❤❤

  • @rideshareescapades4281
    @rideshareescapades4281 11 ปีที่แล้ว

    I love you man
    it's a lot of fun learning this stuff.
    Thanks a lot

  • @cherrychapstickgurl
    @cherrychapstickgurl 9 ปีที่แล้ว +1

    this helped me with psychology! thank u sal

    • @uvwxyz91
      @uvwxyz91 9 ปีที่แล้ว

      +cherrychapstickgurl wut?lol

    • @cherrychapstickgurl
      @cherrychapstickgurl 9 ปีที่แล้ว

      ***** that's right! you need math in psychology too

    • @eugenedeschamps164
      @eugenedeschamps164 7 ปีที่แล้ว

      yha there is is how crazy do you think you patient is and if he going to kill anybody there is a general equation is to start guessing the medication that you think that fits the med book for that diagnoses then again guess the doses you gonna cram down his esophagus the more the better because the more patients you overdose is better for the bank book at the end

  • @lorassa727
    @lorassa727 11 ปีที่แล้ว

    THANK YOU!! Your videos are amazing, such an amazing and intelligent man!

  • @floh223
    @floh223 5 ปีที่แล้ว

    The video is simply beyond cool. Thank you so much sir.

  • @misterwessels
    @misterwessels 13 ปีที่แล้ว

    Thank you very much for this very clear explanation!

  • @AbirChoudhury101
    @AbirChoudhury101 7 ปีที่แล้ว

    Thanks for the explanation!

  • @chaitanyatuckley4666
    @chaitanyatuckley4666 5 ปีที่แล้ว

    Beautiful. Made my day.

  • @karafofubuntu
    @karafofubuntu 11 ปีที่แล้ว

    Thank you so much for a clear explanation.

  • @rachitadehury2829
    @rachitadehury2829 8 ปีที่แล้ว

    Thank u so very much u helped me a lot

  • @J0EH3AD
    @J0EH3AD 14 ปีที่แล้ว

    Thank you for very nice and instructive Probability series. I would like to see mathematical analysis of random walks - will you create it?

  • @NikitaSharma-bs4gg
    @NikitaSharma-bs4gg 3 ปีที่แล้ว

    Thank you 💚💚💚

  • @meghalbhansali5820
    @meghalbhansali5820 3 ปีที่แล้ว

    This was beautiful

  • @quinnculver
    @quinnculver 11 ปีที่แล้ว

    Very nice explanation. Hats off.

  • @firaskais
    @firaskais 6 ปีที่แล้ว

    Did you mean to right the symbol of the mean instead of variance in the center of graph toward the beginning?

  • @quazinuzhat1515
    @quazinuzhat1515 8 ปีที่แล้ว

    you nailed it. thanx a lot