Why Dividing By N Underestimates the Variance

Рет қаралды 124,614

5 жыл бұрын

This is the follow up video to:
Statistics Fundamentals: The Mean, Variance and Standard Deviation
• Calculating the Mean, ...
In it, we show exactly why, when we estimate the variance, dividing by 'n' underestimates the value we are interested in. It also describes why we square each term instead of taking the absolute value. The visuals used in this StatQuest make it easy to remember why we should divide by n-1, and this will save us from falling into a very common pitfall.
If you'd like to support StatQuest, please consider...
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Corrections:
3:23 I should have said "To understand why dividing by n underestimates the variation around the population mean".
3:40 The estimated mean was switched with the population mean.
#statquest #variance

Пікірлер: 613

@statquest 4 жыл бұрын

Corrections: 3:23 I should have said "To understand why dividing by n underestimates the variation around the population mean". 3:40 The estimated mean was switched with the population mean. Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

@Viralvlogvideos 4 жыл бұрын

BAM BUM hahah

@mayurihazarika6550 Жыл бұрын

Please Give Video on degrees of freedom please🙇

@m3c4nyku43 Жыл бұрын

At around 8:35, you should've used asterisk '*' character instead of 'x' character for multiplication. I was a bit confused and thought you wrote 2*(x-v)*x-1 instead of 2*(x-v)*(-1). Great video by the way!

@statquest Жыл бұрын

@@m3c4nyku43 noted

@paulpaschert6215 5 жыл бұрын

is there some sort of award we can give this guy? please?!

@statquest 5 жыл бұрын

@jacobmoore8734 5 жыл бұрын

I think we're encouraged to purchase a double dam t-shirt or sweatshirt, which is more of a financial incentive than an award but who doesn't like getting paid to be awesome? I'll probably pick one up this weekend

@statquest 5 жыл бұрын

@@jacobmoore8734 Thanks! :)

@paulpaschert6215 5 жыл бұрын

@@jacobmoore8734 award + t-shirt = double bam! just ordered my own shirt. gonna wear it to my statistics test in 2 weeks

@karankartik1327 3 жыл бұрын

Really, your way is too unique. one of the best

@arun5351 4 жыл бұрын

Amazing Josh!! I can't imagine how much hard work goes into simplifying the complex statistics concepts and coming up with these amazing videos. And on top of that your ingenious ideas of adding humor and musical creativity, taking the content to another level. If there was an Oscar for tutoring you'd be the undisputed winner. BAMMM !!- simply the best educator on KZfaq....

@statquest 4 жыл бұрын

BAM! :)

@namanjain8939 4 жыл бұрын

I searched for this on a number of online resources, some mentioned "n" while others "n-1", leaving me confused. This is the best possible explanation to the problem you made it really easy for us to understand. Thanks a lot !!! Bammmm subscribed and shared with friends.

@statquest 4 жыл бұрын

Awesome!!! Thank you very much for subscribing and sharing my videos with your friends. :)

@ramkotha4726 3 жыл бұрын

Josh, This is a total hypnotism you did with BAMs, echos, and other sounds. You mastered the art of making us stick there. I been searching for statistics and machine learning videos where they have kind of a roadmap, and simple explanations for complex topics, and this is it. You saved my life for sure, my donation is on its way, I know anything is small for what goes into making these. Hats off to you, you are a LEGEND. We owe you...

@statquest 3 жыл бұрын

Wow, thank you!

@ksrajavel 4 жыл бұрын

Came to this video for "Why Dividing By N Underestimates the Variance" but got to know why absolute values are not used in Variance calculation. Literally cried, Prof. Josh.. Kudos to you. You are supporting me to understand the topics in statistics. I will support you regularly after I get a job soon. And I'm sure your teachings are required for many of the upcoming students in the coming decades. In India we have a concept called "Guru Kulam", and I see you as my guru (Not the term commonly known in the western world, this is more about respect)

@statquest 4 жыл бұрын

Thank you so much!!! It means a lot to me.

@arbanafal 5 жыл бұрын

I have nothing but admiration; this is the clearest explanation that I've seen so far that does not shy away from the underlying math, yet still keeping it understandable for those with minimal math background. I feel like a bit of a fool when I see the contrast between my own attempts to explain this correction factor and your explanation.

@statquest 5 жыл бұрын

I'm glad you like the video so much. Thanks! :)

@nursahidassafaat6283 4 жыл бұрын

I've been 2 years asking how to plot variance, why sample variance (also sd) divided by n-1. And this is best explanation i ever had

@statquest 4 жыл бұрын

Awesome! :)

@mugssyy 3 жыл бұрын

Michael Scott: Why don't you explain this to me like I'm five? Josh Starmer: Bammm!! and understood ... thank you : ) !

@statquest 3 жыл бұрын

BAM! :)

@Deepak-uv8du 3 жыл бұрын

@@statquest Can you provide the slides for all the statistics videos you used to explain the concepts

@statquest 3 жыл бұрын

@@Deepak-uv8du I have PDF study guides for some of my videos here: statquest.org/studyguides/

@wowZhenek 3 жыл бұрын

Yet another video from this channel that leaves me speechless. I've never really understood this concept until I've watched your video. Thank you very much, again.

@statquest 3 жыл бұрын

Wow, thank you!

@libertarianPinoy 5 жыл бұрын

Kids today are so lucky they can review their stats online like this with great teachers.

@statquest 5 жыл бұрын

@ireneylhsiao 4 жыл бұрын

Bam!!! I've watched lots of your videos after I discovered the one explaining the standard error. You make me understand stats concepts more clearly. Please continue making these awesome videos (machine learning too)! 5 dollars donated!

@statquest 4 жыл бұрын

Thank you very, very much. I really appreciate it. :)

@dimiw5435 4 жыл бұрын

the best accessible explanation I can find in the whole internet for this mystery. then just as I was about to say "aha! you missed out something!" towards the end of the video, you seemed to have read my mind and "p.s. if you are wondering why n-1 and not 0.5 or 2 .... " you are so so spot-on!

@statquest 4 жыл бұрын

Thank you very much! :)

@naysannaderi5135 4 жыл бұрын

@@statquest I agree - best explanation i have found and i'm sharing this video with all my students. THANK YOU! So.... any chance that next video is coming out soon? (or has come out already?)

@statquest 4 жыл бұрын

@@naysannaderi5135 I hope the next video will come out soon. Possibly in the next 4 months or so. I hope!

@Ana-wx8jm 4 жыл бұрын

I click the like button before I watch it because I'm always sure I'll love it! Thanks so much for making this series. You'll never know how helpful it has been in my life

@statquest 4 жыл бұрын

Hooray!!! Thank you very much! :)

@GbUnLimiteD 5 жыл бұрын

Yes! I had already feared that the n-? question won't be explained. Glad to hear that you will explain this unsolved mystery in the next video!

@statquest 5 жыл бұрын

Unfortunately, it will be a while before I get to it. I've got covariance and correlation coming up next, then a few machine learning videos, but then I'll loop back to expected values. It's a topic that I've wanted to work on for quite some time.

@2oqp577 5 жыл бұрын

My uneducated guess about n-x is that the bigger the magnitude diff. between the population and your sample size, the larger x would be. Because as this magnitude get smaller and smaller, the need for x to have any significant value, disappears. My biggest question is why would x lead to this unitary value when your sample size is little. But we'll see what Josh explains about that.

@nickp7526 4 жыл бұрын

Intuitively: the number you're dividing stands for the degrees of freedom you have. In other words: how many data points are allowed to vary freely. The reason that this is 1 less here is, as the video hinted at, because of the sample mean. If someone shared with you n-1 data points of their sample distribution of n points, and you know what the sample mean is, then you can easily calculate what the last data point is. I.e. that last data point doesn't have any freedom to vary, just because it was crucial in defining the sample mean. This doesn't matter if you know what the population mean is, precisely because the sample distribution didn't decide its value. Therefore all n values in a sample distribution with known population mean can be used to make an unbiased estimator, while only n-1 degrees of freedom can be used to have an unbiased estimator when all you known is the sample mean. Mathematically: en.m.wikipedia.org/wiki/Bias_of_an_estimator The first example (in the examples tab) shows why it should be n-1, and not n, or n-whatever.

@tippyandfriend 5 жыл бұрын

This is excellent, I am looking forward to the next one.

@anujlahoty8022 5 жыл бұрын

Awesome and the best video with most simplified explaination.

@statquest 5 жыл бұрын

Thank you! :)

@anishchhabra5313 2 жыл бұрын

This is epic, never got a better or clearer explanation for this particular problem. Hats off!🙌

@statquest 2 жыл бұрын

Thanks a ton!

@PraveenKumar-yv5zn 4 жыл бұрын

This is the best explanation that I've come across for this. And I really liked that you gave a proof for general set of observations. Thanks a lot.

@statquest 4 жыл бұрын

Awesome, thank you!

@punktdotcom 4 жыл бұрын

I rather get a clear and understanding explanation with "BAMS" like i'm five, than a 50 pages long explanation with words like "trivial" and abbreviations (q.e.d) and just feel depressed and left clueless. And an other very important thing: Only if you *really* understood the topic, you can explain it with easy words. Very well done, Josh! Thank you very much!

@statquest 4 жыл бұрын

Thank you very much!!!! :)

@brucewayne6744 5 жыл бұрын

Great explanation!! I'm loving every second of your videos!!! Cheers!!

@statquest 5 жыл бұрын

Thank you! :)

@achannel9598 2 жыл бұрын

came from calculating the mean, variance and SD video. Did not expect a proof for why variance = x-bar. This is a really good in depth video i've ever watched for statistics. Thank you very much.

@statquest 2 жыл бұрын

bam!

@chathurijayaweera1590 2 жыл бұрын

Thank you for this explanation. When I was learning stat in university, I did not understand well, why we divide by (n-1) instead of n to estimate sample variance. You explained it so clearly in a way that I will never forget what I learnt. Thank you Josh !!!

@statquest 2 жыл бұрын

Hooray! :)

@keej7146 10 ай бұрын

Thank you for this!! The first time I saw the formula for the sample variance I wondered why the n-1 was there, this is a great explanation.

@statquest 10 ай бұрын

Thanks!

@Calypso-rt5tf 10 ай бұрын

hello, keej i hate u mate

@jsc3417 4 жыл бұрын

Thank you, 10 years of confusion made clear by this 15 mins of video.

@statquest 4 жыл бұрын

Hooray! I'm glad the video was helpful. :)

@lelamakharadze727 5 жыл бұрын

"Future is nooow, BAM " - #LOL #respect #welldone #thanks

@statquest 5 жыл бұрын

Thank you! :)

@Michael-zn4oq 3 жыл бұрын

Thank you so much for the clear and simple explanation. This is an example for when showing the proof is better than only trying to give an intuition.

@statquest 3 жыл бұрын

Thanks

@morenomartinovic4385 4 жыл бұрын

I'm eagerly awaiting the expected values quest! Thank you so much for making these videos, I love watching them before sleep.

@statquest 4 жыл бұрын

Awesome! It's on the to-do list, but it might not be done for awhile. :(

@morenomartinovic4385 4 жыл бұрын

@@statquest That's cool, take your time to keep making awesome videos. I still have loads of your videos on my to-watch list!

@HamidNourashraf 2 жыл бұрын

I love the way you explain these topics, great work!

@statquest 2 жыл бұрын

Thanks!

@emmaning992 4 жыл бұрын

I admire this explanation... Amazing. I really look forward to the expected values video!

@statquest 4 жыл бұрын

Thank you. I started working on the expected value video, but it will still be awhile before I finish since I have many other projects to work on.

@killua9369 2 жыл бұрын

I have always hated statistics but I just today found this channel and this guy explains everything elegantly! ❤😊

@statquest 2 жыл бұрын

Wow, thank you!

@ryanmckenna2047 Жыл бұрын

This channel is just incredible, well done!

@statquest Жыл бұрын

Thank you very much! :)

@tumul1474 4 жыл бұрын

Statquest, JBstatistics and Khan Academy.....You guys are just amazing !!.....Thank you for all you have done for us

@statquest 4 жыл бұрын

Thank you! :)

@izebit 4 жыл бұрын

Thank you, I haven't known about these channels

@davidh1876 5 жыл бұрын

Big thanks from Taiwan. I have been asking why not dividing by n since high school...but all I get from my teacher was only "a rule of thumb". Now I know the reason behind and thanks to statquest. BAM!!

@statquest 5 жыл бұрын

Hooray! :)

@alexandermedina4950 3 жыл бұрын

I can only have love for these videos, thank you Josh and all the team if you have any.

@statquest 3 жыл бұрын

Thank you! It's just me doing all this.

@cristianleoni6852 4 жыл бұрын

Amazing explanation of why we use the square of the errors instead of the absolute value! I always asked myself that and all the teachers said it was just to give a bigger weight to the errors! We need the statquest on expected value!

@statquest 4 жыл бұрын

Thanks! I'm working on the expected value, but it still might be a few months before it's ready.

@theblinkingbrownie4654 6 ай бұрын

I think for even n there wouldn't even be a minimum point, rather a flat line between the 2 middle samples

@haoqichen7610 2 жыл бұрын

The last point about absolute value explains a lot! I was always wondering why squaring data is so much more common than taking absolute values!

@statquest 2 жыл бұрын

bam! :)

@nizarch22 3 жыл бұрын

I don't even remember what I was confused about in particular, but I remember feeling very happy to see this video. Will revisit this in the following days. Psst, you're a gem ;)

@statquest 3 жыл бұрын

Thank you very much! :)

@Drugio24 5 жыл бұрын

this is literally what I was trying to get a clear understanding on in the last few days? what are the chances? no seriously what are the chances?

@statquest 5 жыл бұрын

That's awesome! :)

@ARM26878 2 жыл бұрын

BAM! I have not seen this concept explained better anywhere else ever. Have you gotten around to making the follow-up video on 'expected values' ? Can't thank you enough for your channel

@statquest 2 жыл бұрын

I've got the video on expected values kzfaq.info/get/bejne/gbKjkpqTnLmvmWg.html and kzfaq.info/get/bejne/hbmApZl4m7HFXYk.html , but there are still a few steps to go after that... :(

@thegamingannex5752 2 жыл бұрын

Your work is impeccable. BAM!

@statquest 2 жыл бұрын

Thank you!

@ginopeduto4264 4 жыл бұрын

THX!!! Looking forward for the STATQUEST on expected Values ;))))

@statquest 4 жыл бұрын

Me too!

@yildizkoca8878 2 ай бұрын

This video is such a gem! Thanks for explaining the root of this concept which is not easy to find even in statistics books.

@statquest 2 ай бұрын

Glad it was helpful!

@dver7349 11 ай бұрын

Super interesting! Thanks for your work!

@statquest 11 ай бұрын

Thanks!

@magtazeum4071 2 жыл бұрын

8:22 `the way he said "Whaat" is so cute.. I'm in love

@statquest 2 жыл бұрын

@Lsazeh 2 жыл бұрын

Thanks so much for the explanation, super clear as always

@statquest 2 жыл бұрын

Glad it was helpful!

@mukhtarbimurat5106 Жыл бұрын

Greatest explanation so far!

@statquest Жыл бұрын

Thank you! :)

@rajarshibasak347 12 күн бұрын

Aah! Finally end. What a excellent work by you!! Statquest rocks ❤.. Thank you sir. You helped a lot in my carrier ❤.

@statquest 12 күн бұрын

Thanks!

@ROTOBAfilms Жыл бұрын

You are a very great teacher, i like your coaching style, keep going on!

@statquest Жыл бұрын

Thank you! 😃

@nidhiarora4739 3 жыл бұрын

I have been SO stressed out about a project I'm working on, and 3:15 made me laugh so hard!!! I didn't even realize how stressed out I was until I caught myself laughing for the first time in weeks. Thank you Josh!!! **sob**

@statquest 3 жыл бұрын

Hooray!!! Good luck with your project. I hope it goes well. :)

@mansoorbaig9232 4 жыл бұрын

This is awesome explanation. Waiting for quest on 'Expected Values'....BAM!

@statquest 4 жыл бұрын

Me too. Hopefully I can get to it soon.

@edward8064 3 жыл бұрын

Mind = Blown. Thankyou from Indonesia.

@statquest 3 жыл бұрын

Thanks!

@christopherchen4920 3 жыл бұрын

The most impressive explanation I've ever seen.

@statquest 3 жыл бұрын

Thanks!

@koreanbroadcastarchive306 3 жыл бұрын

Excellent. Thank you for a great explanation.

@statquest 3 жыл бұрын

Glad you enjoyed it!

@vkvkvkvk 5 жыл бұрын

baaammm! subscribed.

@statquest 5 жыл бұрын

Awesome! :)

@nursahidassafaat6283 4 жыл бұрын

BAAM! me too

@keysky_1622 5 жыл бұрын

wow that n-1 has something to do with E(X)? Im waiting for it!

@Igor-vb1hv 3 жыл бұрын

Thanks for explanation! I understand that differences between the SAMPLE data and the sample mean are smaller than the differences between the SAMPLE data and the population mean. BUT! We are not interested in the difference between the SAMPLE data and the population mean, rather we are looking for the difference between the TRUE POPULATION data and the population mean (the population variance). And it's not clear why this value would be larger. I mean sample data is centered around sample mean the same way population data is centered around population mean. Comparing sample data with population mean feels to be misleading.

@statquest 3 жыл бұрын

The best estimate we can do is the estimate of the variance around the sample mean, which is probably an underestimate, but not always. So this is the best we can do.

@ipmankus 4 жыл бұрын

Very nice explanation, god bless you josh!

@statquest 4 жыл бұрын

Thank you! :)

@yufeizhan726 3 жыл бұрын

I finally know why n-1 is used. Thank you so much!

@statquest 3 жыл бұрын

Bam!

@spiritualityandscience 3 жыл бұрын

Perfect !!! thanks for posting.

@statquest 3 жыл бұрын

Thanks!

@OdysseusKingofIthaca-o4n 28 күн бұрын

Thank you St Josh for this illuminating explanation :)

@statquest 28 күн бұрын

My pleasure!

@mahboobalam5689 5 жыл бұрын

Great as always! Thanks Prof.

@statquest 5 жыл бұрын

Thanks! :)

@mahboobalam5689 5 жыл бұрын

@@statquest I know that you have some videos on quantiles on your channel. I was wondering if you could think about the possibility for a video on quantile regression and its implication possiblities in genetics, especially in population genetics. I have found some resources on youtube and through online which mainly focuses on social sciences. Anayways, thank you again.

@elenieXQ 4 жыл бұрын

thank you and this is very helpful!!

@statquest 4 жыл бұрын

I'm so glad!

@lyrachang950 8 ай бұрын

im currently learning data analytics and trying to figure out ab testing and bam! here i am! thank you so much for making statistics fun and easy to understand! double bam!

@statquest 8 ай бұрын

Happy to help!

@shashankupadhyay821 4 жыл бұрын

I usually hit like after the first BAMMM. This is some super great stuff Josh.

@statquest 4 жыл бұрын

Thank you very much! :)

@GurunathHari 5 жыл бұрын

Brilliantly explained....

@statquest 5 жыл бұрын

Thank you very much! :)

@zinnijha7556 2 жыл бұрын

Awesome and Thank you!

@statquest 2 жыл бұрын

No problem!

@Marius-vw9hp 4 жыл бұрын

I wanted to know why we deduct exactly 1, but I guess that only takes 20 aditional minutes to explain. Hooraay! Thanks for the videos :)

@statquest 4 жыл бұрын

It's true. We have to dive into expected values and that is a whole new topic.

@andersonbessa9044 5 жыл бұрын

Your videos are so helpful

@statquest 5 жыл бұрын

Thanks! :)

@groovearmada2008 4 жыл бұрын

Has the announced video "expected values" been released? I couldn't find it... Thx

@statquest 4 жыл бұрын

Not yet, but I'm working on it.

@Ujjwalchhabra1 4 жыл бұрын

You left in a cliff hanger of expected values :(( Love your videos tho, thanks for these!

@statquest 4 жыл бұрын

I'm working on it, but everything I do takes longer than I would like. :)

@alishashingade4456 3 жыл бұрын

You are so awesome ! Thank you Josh :)

@statquest 3 жыл бұрын

Thank you! :)

@NuclearSpinach 3 жыл бұрын

"The future is now" I'm dying

@statquest 3 жыл бұрын

BAM! :)

@marinasha2949 Жыл бұрын

Good job Josh!! Waiting for StatQuest on Expected Values! I am the one wondering why not dividing by 'n-0.5' or 'n-2'

@statquest Жыл бұрын

Thanks!

@timothymattnew 2 жыл бұрын

I really want to understand why we use n-1 instead of substituting any other number instead of 1. I'm guessing it has something to do with the way we approximate the mean and the variance. I think it's related to properties the normal distribution has and such. I think that to truly understand that analytically I'd have to integrate over all possible outcomes while taking into account all the probabilities and then calculating the average. It really excites me, but I don't know where I can find the information needed to understand the subject in more depth. Can you give me some advice on what textbooks I should read, please? I'd really really appreciate that!

@statquest 2 жыл бұрын

See: online.stat.psu.edu/stat415/book/export/html/886

@timothymattnew 2 жыл бұрын

@@statquest thank you, I will definitely read that!

@ThalesBrunoM 4 жыл бұрын

8:21 -> I will watch a thousand times and I will laugh out loud a thousand times 😂

@statquest 4 жыл бұрын

Hooray! :)

@Lets_MakeItSimple 5 жыл бұрын

Hey josh, yet another cool explanation.

@statquest 5 жыл бұрын

Thank you! :)

@chiragsomani101 2 жыл бұрын

ASTOUNDING EFFECTS & EXPLAINATIONS! SUBSCRIBED TRIPLE BAM!!!

@statquest 2 жыл бұрын

bam!

@shouryanand456 4 жыл бұрын

I wish you were my stats teacher!! Amazing job!!!

@statquest 4 жыл бұрын

Thank you! :)

@shouryanand456 4 жыл бұрын

@@statquest really waiting for the expected value video to get explanation of n-1. When can we expect it?

@statquest 4 жыл бұрын

@@shouryanand456 Unfortunately, it might be a while. I've got a full plate until after the summer.

@coldbrewed8308 5 ай бұрын

Oh no... I'm falling deeper and deeper into this rabbit hole

@statquest 5 ай бұрын

@sephirothjc 2 жыл бұрын

This the best explanation ever

@statquest 2 жыл бұрын

Thank you!

@yajan6650 2 жыл бұрын

This is Amazing! BAM!!

@statquest 2 жыл бұрын

Thanks!

@palmyk7114 4 жыл бұрын

Thanks a lot!

@88skewer 3 жыл бұрын

awesome video, do you have any recommended channel to learn derivative and calculus ?

@statquest 3 жыл бұрын

I have a video on The Chain Rule Here: kzfaq.info/get/bejne/rdJhoNyp19q1eIU.html but I have heard that Khan Academy is good for learning derivatives.

@fakhrealam502 4 жыл бұрын

I love your video's... DOUBLE BAM !

@statquest 4 жыл бұрын

Thank you! :)

@shubhamtalks9718 4 жыл бұрын

Man, you are great. From where did you learn these concepts? Keep making videos and enlighten us. Thank you.

@statquest 4 жыл бұрын

Thanks! :)

@shubhamtalks9718 4 жыл бұрын

@@statquest When I try to learn these concepts they seem complicated to me. From where did you learn these concepts?

@statquest 4 жыл бұрын

@@shubhamtalks9718 The concepts seem complicated because people that do not really understand them try to teach them. How did I learn them? Years of really hard work. I read everything I can about a subject, then I re-read it. Then I re-read it again. Then I make a program based on my ideas and see what happens. Then I re-read everything over again. And sooner or later I figure it out. But it takes a lot of time and a lot of work. Sometimes I worry I will not succeed, and sometimes I fail, but I keep trying anyway.

@shubhamtalks9718 4 жыл бұрын

@@statquest Thanks😁

@sourabh513 2 жыл бұрын

Great video! Can you share link of StatQuest on Expected Values that explains why divide by n-1 and not n-0.5 or not n-2? Thanks!

@statquest 2 жыл бұрын

I hope to do that one day.

@MrBlissTube 4 жыл бұрын

Great video! Where is the one about Expected Values? I cannot wait with such a cliffhanger! GoT finale can wait...

@statquest 4 жыл бұрын

Very funny! Yes, I have my work to do. I hope to get to expected values before too long.

@MrBlissTube 4 жыл бұрын

@@statquest Thanks a lot for responding! ... and sorry, as I noticed after reading more comments, that you had already answered this question many times. Quest on!

@inkevinsshoes4690 3 жыл бұрын

Great video! Which book did you get this explanation from?

@statquest 3 жыл бұрын

Ummm....I just did the math.

@aanchalagarwal6886 4 жыл бұрын

Thank you! These videos have really helped me in understanding the concepts clearly. However, I wanted to know if you have uploaded the video on Expected Values and if you could provide the link to the same.

@statquest 4 жыл бұрын

I haven't uploaded the expected value StatQuest yet, but I am working on it.

@aanchalagarwal6886 4 жыл бұрын

@@statquest Alright. Thank you

@scuti7073 2 жыл бұрын

Man, I always thought that statistics doesn’t make any sense at all and that people should just blindly chug into weird formulas without questioning, but this was absolutely mind opening. Not even khan academy could explain the proof!

@statquest 2 жыл бұрын

Thanks!

@ankitvyas9013 Жыл бұрын

This is gold.

@statquest Жыл бұрын

Thank you!

@fernunez2131 2 жыл бұрын

I love the humor included in this videos, hahahah!

@statquest 2 жыл бұрын

Thanks!

@anandrathi871 4 жыл бұрын

I do understand the way yo calculate min variance But @ 14:54 How did you conclude in that "Thus valus around sample mean is always less than population mean" ?

@statquest 4 жыл бұрын

Because the sample mean is the value that minimizes the variance, any other value will give you a larger variance.

@lambdamax 4 жыл бұрын

Is the statquest for expected values not out yet?

@statquest 4 жыл бұрын

Not yet.

@MirrorNeuron 8 ай бұрын

Hi Josh, where did you study about it, is it from Bessel's correction or Karl Pearson. I am interested to ready a bit about the history behind it. Can you please suggest a book or paper where the original discovery was made. Thanks in advance.

@statquest 8 ай бұрын

The idea for this came from Bessel's correction.

@wexwexexort 4 жыл бұрын

Waiting for StatQuest on Expected Values.

@Deepak-uv8du 3 жыл бұрын

Can you provide the slides for all the statistics videos you used to explain the concepts

@statquest 3 жыл бұрын

I have PDF study guides for some of my videos here: statquest.org/studyguides/

@izebit 4 жыл бұрын

Brilliant, love your channel 👏 I don't understand this moment 8:59. How is x variable simplified? It seems to me I am stupid. Anybody can help?

@statquest 4 жыл бұрын

The "x" variable isn't simplified, instead, the whole equation is simplified. All we did was rearrange the terms so that it will be easier to take the derivative.