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Introduction to the Central Limit Theorem
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- čas přidán 27. 12. 2012
- I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a non-technical treatment, and simply illustrates the important implications of the central limit theorem.)
For those using R, here is the R code to find the probability for the example in this video:
Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000:
1-pnorm(66000,62000,32000/sqrt(100))
[1] 0.1056498
Or, standardizing:
1-pnorm((66000-62000)/(32000/sqrt(100)))
[1] 0.1056498
1-pnorm(1.25)
[1] 0.1056498
I'm a statistics professor in the Department of Mathematics and Statistics at the University of Guelph.
I wish you were my prof. Also can you do videos on Moment generating functions?
Many thanks from York University
@@sanchitakanta1018 LOL
Informative Video. Keep moving making new videos
Hello sir
My teacher has spent hours trying to teach us this. You did this in 13 minutes and 13 seconds.
Great job and thank you:)
Hey just curious what are you pursuing now ? (as you were studying stats 5yrs ago)
The world need to know😂
😂here for this
Watching in 2020 for my stats diploma. Just realized this is an 8 year old video. Jeremy Balka, your channel is a gold mine. You are amazing! I will always remember you. Thanks!
Thanks for the feedback. I'm a little overly restrained in this one, and possibly a touch boring, but I felt that the original was a little over the top and irritating in some spots. I'm glad you liked the normal distribution video! Stats is definitely something to get excited about!
thank professor! Your video makes me a big step to keep fire learn statistics!!!!
I never really comment on videos but this was so helpful It would be an insult to not thank you. So, THANK YOU! You have saved me
There are different formats of standard normal table. I have videos outlining how to use a standard normal table for two main types of standard normal table (one that gives the area to the left of the value of z, and the other that gives the area between 0 and a positive value of z).
Extremely, extremely helpful. I'm going through a data science masters and I'm finding myself increasingly turning to youtube and getting a primer/intuition of a concept before listening to my actual lectures. This week is CLT and law of large numbers and after this video I'm in a lot better shape to assimilate the material. Thank you!
Very well explained, and good examples! I find examples are extremely important to learn stats, so this helped.
Thanks! I'm glad you found it helpful.
Best video on Central Limit Theorem. Do you have a virtual tip jar I can throw some virtual dollars in?
Thanks for the compliment. I'm just glad I can be of help. Cheers.
@@jbstatistics what a legend
@@jbstatistics I think I can speak for everyone when I say that we collectively refuse. Please give us a tip jar 😂
@@jbstatistics In the last example while we are calculating the probability of the average being greater than 1.25 sigma.
The average is always in the middle of the normal distribution right?
Z value =0.
Then how can it be greater than 1.25 Sigma?
Can you please explain.
@@sanchitakanta1018 You're mixing up the true (theoretical) mean, and the sample mean. The normal distribution is centred at the true mean. The question asks for a probability involving the sample mean.
Thank you so much for these videos. I am taking stat for engineers and I am literally teaching myself everything by watching your videos.
Woke up, checked this Vidéo before even have my coffee, I knew C.L.T longtime ago but now I go it much better. now I can explain it to my daughter in a btter bay . Thanks you .
My former statistics professor (great dude) used to say that without central limit theorem, we wouldn't be here. I laughted then, I cried over my tests, then I eventually learned... and everything makes sense once we realize the awesomeness of this mathematical theorem. Now I do the same for my colleagues :)
When we draw a single sample, the sample mean will take on a single value. But if we were to draw a different sample, the sample mean would take on a different value. Before we draw our sample, we can think of the sample mean as a random variable with a probability distribution. The CLT tells us something about that probability distribution. You might want to watch my video "Sampling Distributions: Introduction to the Concept", which discusses this notion in greater detail. Cheers.
the number of views in this channel does not match the number of subscriptions . This guy should have more than a million subscritptions . i come here whenever i get confused about something , thanks dude and greetings from Algerian Sahara
Best Video explanation on CLT on the whole youtube. Thanks a lot
tbh literally the best video on CLT I've ever watched, thank you so much, thank those statisticians so much
I love you so much man! I'm studying for the CFAs and your video explained CLT perfectly :D
Thanks! I'm glad I could be of help!
Best video series about statistics in this whole youtube wildlife, thank you so much for existing and making everything better
This is magic how you taught us this difficult concept easily.
I use your videos as inspiration when I prepare for teaching my class - thank you for the perfect explanation
I'm glad to hear that! Thanks so much for the compliment!
I can’t tell you how thankful I am of this video!!!
I'm glad you found it helpful!
You sir deserve a medal for explaining this stuff in a 13 minute video!! I was so confused.. thanks !!!!!!
You are very welcome!
One of the best video for understanding CLT.. thanks a lot...!!!
Thank you so much for these videos. Between the textbook and my professor, I could NOT figure this out till I watched your video. They have been so helpful, especially with everything being online/ remote now.
you're a fucking god of explanation!
Thanks!
Houna Mao
True that!
I have been watching many of your videos recently. Thank you for your (fast) videos as well as you explain them very clearly with your voice. Enjoyment to watch and learn!
All your videos I watched are concise and simple. I do not think any of the concepts can be explained more simpler. You are amazing teacher
Thanks!
Thank you very much for your admirable kindness. Your explanation is so comprehensive that I can save much time.
I have been confused for years but not anymore. Excellent explanation! Thank you very very much.
I'm glad to be of help!
I learn more in 13:13 with your explanations than three hours in class each week plus tutoring.
I'm glad I could be of help!
God Bless You! I am a little more confident about the final exam after watching your series of videos! Thank You!
This was super helpful, thank you! I like how clearly into statistics you are. Really helps me to pay attention.
Thanks! I'm glad to be of help!
For what it’s worth, I would just like to let you know that your hard work does not go unappreciated!
Bravo. His teaching is beyond perfection. Amazing.
I have an stat exam tommorow.. You saved me... Thank you so much Sir :)
Amazing way of explaining CLT. Thank you so much!!
You're welcome, and thanks for the compliment!
Very good video! It tells us why CLT is such important. I was wondering whether you could make another video explaining the CLT intuitively? Why the limiting distribution is normal instead of exponential, gamma, or any other distributions? What is the essence of the CLT?
You make the best videos. You may not touch on all the topics that others do, but the fact that you have one of the lowest number of subscribers on CZcams is criminal. I hope that changes because your focus to simplify and emphasise certain points within a topic is second to none. Thank you and please keep them coming.
WOAAAHH NICE BOY!!! This will exactly helps me to pass tomorrow's exam...
Very well explained, i would recommend this to everyone that is banging their head on the wall, trying to figure out. Thank you
Thanks for the kind words!
I just keep coming here despite all the textbooks I keep buying! Thanks so much again for being on Yotube.
You're very welcome!
i love how this is just straight to the point. I hate when videos and BOOKS always start with an example. just give me the god damn definition already! so thanks.
I really appreciate these videos, I hope to be a teacher who can help my students understand as well as you do.
Really helpfull, my book on statistics tends to be very formal. With these videos i understand it a lot quicker.
Thanks from an electrical engineering student.
+hijdiegaapt You are very welcome!
Your videos are as good as Khan Academy. Thanks for helping us with the maths!
The best and clearest explanation I have ever found!!!!!!!!
Keep the good job #######
Thanks so much for the kind words!
This channel never disappoints.
This is amazingly beautiful. How am I going to tell my mentor "please watch this video" :) Thanks for crystal clear explanation with robust example.
Hi Karthik. It is the number of observations used to calculate the mean that is important. In practice we typically draw only a single sample. If that sample has 5000 observations, say, and our sample mean is thus the mean of 5000 observations, then the sampling distribution of the sample mean will be approximately normal in that situation.
Hi Vinayak. In its simplest form, the CLT applies to the mean of independent and identically distributed random variables. If we are sampling from a finite population, then if the sampling is done without replacement the observations are not independent. So to perfectly satisfy the conditions of the CLT, we'd need to be sampling with replacement. But if we are sampling only a small fraction of a large finite population, then there isn't much of a difference between with and without replacement.
Definitely the best video on explaining CLT! Thank you!
I have learnt so much watching your statistics videos. Thank you for sharing your insight on the subject
i wish you could replace my professor. perfect explanation. i understood the concept just by watching it once. best video on central limit theorem on CZcams!
I just tried the video, and it plays all the way through for me. You're the first person to bring up a possible problem, so there's a good chance it's a problem on your end. Perhaps try it in a different browser, or after rebooting, or on another computer. I'd like to know if there's a problem, so let me know if you can't sort it out.
How can you find more of my videos? You can search my channel, or look through the playlists. I don't have them organized on a website just yet.
Thank you so much for this video, especially the word problem that you gave. It helped me pinpoint the main idea of this topic. You are such a blessing for learners during this quarantine. Thank you very much.
Best video this far on the CLT! I have watched around 10. This one did it.
I'm glad to be of help. Thanks for the compliment!
Really explicit explanation! good job!
+Weiji Hong Thanks!
Weiji Hong I don't think you know what explicitly means
Thanks for the compliment! I'm glad you liked it, and I'm very glad to be of help!
Nice to have a Canadian Professor.
Oh boy, an animated channel dedicated only to non simplistic and organized statistics lessons. Thank you jesus
I'm glad to be of help!
This is all finally making sense! 😀 After many years of sort of getting this I understand it now so much better. So basically Xbar is a random variable all of it's own, with it's own mean and s.d ect, and varies depending on which sample we randomly pick from the population right? When I think about it like this it makes a lot more sense. Thanks for these brilliant videos.
Thank You!Its been Years since the Video has been Uploaded,But still Thanks!!
clear, concise and professional. perfect lecture.
+garthenar Thanks!
Clean sweep!! Clarity is wonderful!
Crystal Clear now. GJ!
Hi Vinayak. The very last example involves the average salary of 100 employees. The distribution of individual salaries is probably not normal, but the central limit theorem tells us that the distribution of the mean salary of 100 employees will be approximately normal. That's what allows us to calculate an approximate probability based on the normal distribution. We're drawing a single sample, as we typically do, but it's a single sample of 100 employees.
You are very welcome, and I'm glad to be of help!
WOW ! nice explanation ! easy, understandable and well described !
Thanks!
Hey man, I've been watching some of your videos and they have really helped me to understand better statistics. In the past it seemed so difficult to me, but thanks to you I'm making good progress. I hope you are doing fine :)
Awesome explanation on WHY the CLT is important! >_
Great explanation, which means you know very well what you are teaching. Thanks!
Thanks for the compliment!
You are very welcome Tobias! I hope your studies are going well!
Great video! I mised the lecuture on CLT in math class due to jury duty. This video helped so much!
i finally get the idea of the central limit theorem.Thanks!!!!!
You're welcome! I'm glad I could help!
You're welcome Jessica! Yes, that's correct. There's no way to find that probability without more information.
Great example! Helped me understand why CLT is used
I like the original version of this video better because you seem so excited in it. It makes learning stats fun because it makes the subject seem so much more approachable and maybe not the train wreck you're expecting. I actually got excited about normal distribution! :)
Excellent!. I'm a Statistics teacher and I'm a fan of simulations as replacement of delirious formulae elaboration. There'll be time for that later....
Thanks for the compliment!
Best explanation so far!
It's only reasonable to use a normal distribution to find a probability if your random variable is approximately normally distributed. If, say, the distribution was actually strongly skewed, but we based a probability calculation on the normal distribution, then we could be way off the mark. Since salaries tend to be skewed right, it's not reasonable to use the normal distribution for a probability calculation regarding a single individual.
Thank you so much for clarifying me such an important concept of statistics!
You are very welcome!
awesome dude ! especially the "this quesion cant be answered like that" part haha
I have watched like 10 videos about CLT but this one is the most instructive. But I didn't understand where the formula at 11:28 came from. I understood its logic; when the sample size increases, the standard deviation of sample mean distribution decreases. Because the mean value will be more precise.
Thank you for this great video🤍.
So beautifully explained....
Thank you so much, Sir....
Thanks. Awesome tutorial and example.
You are very welcome. Thanks for the compliment!
Using a standard normal table, you should be able to find that the area to the left of 1.25 under a standard normal curve, rounded to 4 decimal places, is 0.8944. In the example in this video, we need to find the area to the right of 1.25, which is 1-0.8944 = 0.1056. If this doesn't make sense, you're going to have to spend some time reviewing how to use a standard normal table.
In R, to get the answer he mentioned at the end, you would do: 1 - pnorm(66000, 62000, 32000/sqrt(100))
That's great Vinayak! I'm glad to hear it!
it did honestly help. and I have an exam in two hours!! thank you!
Thank you very much,
Understood every single thing..!! (Y)
thank you so much, statistics strats to make sense for me
you are an amazing teacher! thank you very much!!
You are very welcome Omy0my! Thank you for the compliment!
love this !
im like binge watching all your vids .
Thanks! I'm glad to be of help!
Thank you so much for the beautiful explanation! It helps me a lot, I'm not kidding.
The best explanation ever!
+Alex Pereira Thanks!
Wonderful Explanation, thanks a lot
Hi Vinayak. I can't help you there. I might answer a question here or there to clarify a point on a video, but I definitely don't have time to offer tutoring or statistical consulting services to the world at large. Cheers.
Really clear explanation. Thank you a lot! I have understand this more!