Variance and Standard Deviation: Why divide by n-1?

This video covers a few pesky concepts that are often glossed over.

0:00 Variance and standard deviation recap
2:39 Why do we bother with "variance" at all (ie. why square stuff)?
6:55 Why do we divide by n-1?
10:47 What do we mean by degrees of freedom?

Spreadsheet downloadable here:

[leogomes]

I've spent a day looking for an intuitive and satisfactory explanation for n-1 and this is the only one that really did it for me. For some reason, no one else bothered to explain why exactly the numerator with x̄ would always yield the least possible variance. Thanks a lot!

[Nrmad]

Thanks so much for this. It is mostly very clear. My only comment is that in the degrees of freedom section, it should have been made clear that the table on the left is just 3 observations from the wider population and not representative of the entire population. Otherwise, I (and at least a few people in the comments) assumed that that table *was* the population and could not understand why the third value could be equal to 50 while the Mu still remained 53. I had to look through the comments to get clarification that in fact that table on the left is just the *first three* observations from a *wider* population.

[Privacy-LOST]

"Degrees of Freedom tend to be handwaved away by lecturers and tutors alike" => Amen to that ! I still remember how real satisfactory explanations to that were so lacking. Thanks

[mauriciojosericoquiroz]

Dude, you're great your explanations of these concepts are terrific and very easy to follow. As an actuarial science major this is one of the most helpful videos I've ever found.

[KhelderB]

Answered my questions about absolute value! Just re-learning Mathematical statistics currently and these videos are really helpful for motivation and understanding.

[durarara]

You deserve waaaay more subscribers than you currently have. Really well-made videos and nice explanations. Thank you!

[prateek]

you have won my heart... i couldnt find an explanation anywhere for this ... Thank you so much

[jmsherry]

I teach programming for a living. I need to learn stats for ML. This vid is AWESOME! SO clear and well presented! Amazing teaching!

[blubblubber]

Simply great, even brings up questions and clarifys them that I haven't even thought about, but which are kind of important for understanding.

[hugaexplit]

I googled why need to divide by n-1, browsed several sites until I landed here.
Thanks for great explanation.

[ankurkulshrestha]

I watched many such videos, all said almost the same stuff what you said but I ended up all videos with confusions.
You explained it so well that finally I understand the main concept. Thanks a lot.

[krimsonsun]

THREE FREAKING MONTHS OF CLASS!! 10:00 You ended my frustration in 5 minutes.. THANK YOU!!

[payalrana]

You are doing a great job really. Please continue doing it irrespective of the fact of the number of subscribers or likes.You are just amazing.❤

[shashankpatel]

The best ever explanation I found after searching hundreds of sites and links...keep it up man!!!

[adrienjorris]

I'm gonna ship you a dozen packs of golden gaytime ice creams ! Thanks a bunch !

[gustavstreicher]

I like the video. You mention that we shouldn't use the absolute value for describing the spread of the data. The reason why this isn't done is not because it is incompatible with the "higher-order" statistics, but rather because most of statistics was developed with variance in mind. You could just as well develop the parts of statistics that lack looking at the absolute value, which is the L-1 norm. Netflix used an optimization algorithm which made use of this type of norm, which proves that it has practical application. You could also say that if the absolute value squared and cubed, etc. are important, then the absolute value itself must be important as well. They might have different uses, but you cannot say one is better than the other.

[solanki]

I always thought one of the reasons for dividing with n-1 could be that since we're using the sample mean which could be one of the possible values for the population mean so subtracting that one value from the total population thus n-1. That is my way of rationalizing this fact as you mentioned lecturers tend to shrug away from having conversation but since you've explained it so well that that is not the case, I wonder what could be the rationale behind it and not just the fact that it gives the best possible estimate.
Nevertheless, I really like your videos it answers all of my big as well as small doubts I could think of which didn't always have a straight forward answer. Thank you and keep up the good work!

[juliecongress]

Yay ZedStatistics. These videos are so very valuable to help understand concepts. Great supplemental to classwork! Thanks Justin!

[andyduncan]

Thanks for explaining that. Especially the quick degrees of freedom at the end. I knew conceptually why I had to do n-1 with sample sets for getting closer to the real answer, but the degrees of freedom helped me know why that is a thing.
Cheers

[AmitSingh-utwt]

One of the best video for understanding the actual meaning of the variance. Thanks a lot.