Why Dividing By N Underestimates the Variance

This is the follow up video to:
Statistics Fundamentals: The Mean, Variance and Standard Deviation

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.

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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

[statquest]

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.

[paulpaschert]

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

[arun]

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 YouTube....

[namanjain]

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.

[ramkotha]

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...

[ksrajavel]

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)

[nursahidassafaat]

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

[arbanafal]

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.

[dimiw]

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!

[wowZhenek]

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.

[achannel]

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.

[keej]

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.

[davidh]

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!!

[punktdotcom]

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!

[jsc]

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

[ireneylhsiao]

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!

[Ana-wxjm]

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

[chathurijayaweera]

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 !!!

[GbUnLimiteD]

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!

[cristianleoni]

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!