Introduction to the Central Limit Theorem

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

[jbstatistics]

I'm a statistics professor in the Department of Mathematics and Statistics at the University of Guelph.

[yagayagaBabaYaga]

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!

[damiankonieczek]

My teacher has spent hours trying to teach us this. You did this in 13 minutes and 13 seconds.
Great job and thank you:)

[jbstatistics]

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!

[ucheumolu]

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

[musclesmalone]

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!

[samad.chouihat]

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

[mathhack]

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 .

[parthbhatia]

Amazing way of explaining CLT. Thank you so much!!

[jbstatistics]

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).

[themathguy]

Best video series about statistics in this whole youtube wildlife, thank you so much for existing and making everything better

[senorfootball]

Very well explained, and good examples! I find examples are extremely important to learn stats, so this helped.

[icathianrain]

tbh literally the best video on CLT I've ever watched, thank you so much, thank those statisticians so much

[sammendimasa]

Thank you so much for these videos. I am taking stat for engineers and I am literally teaching myself everything by watching your videos.

[jaekl]

You sir deserve a medal for explaining this stuff in a 13 minute video!! I was so confused.. thanks

[manutdsparta]

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!

[ratikeshsharma]

This is magic how you taught us this difficult concept easily.

[gialinhpham]

Thank you very much for your admirable kindness. Your explanation is so comprehensive that I can save much time.

[betsegawlemmaamersho]

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

[emadharazi]

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 YouTube 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.