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Review and intuition why we divide by n-1 for the unbiased sample | Khan Academy

Frames Review and intuition why we divide by n-1 for the unbiased sample | Khan Academy

Description Review and intuition why we divide by n-1 for the unbiased sample | Khan Academy

Comments Review and intuition why we divide by n-1 for the unbiased sample | Khan Academy

Why do we not use |Xi - x̄ | instead of (Xi - x̄ )² ? Comment from : Julio Cesar Jovelina

What if you take the 3 highest values? Comment from : Julio Cesar Jovelina

6:10 Why we divide by n - 1 in variance Comment from : Kevins Math Class

whos this man? he knows so much and explains so majestic I wonder why he does not have a statue in the main square of my city ? he deserve a few Comment from : Dann

That was unclear Comment from : posthocprior

thank you sal :4) Comment from : carlneedsajob

N-1 is "better", but it is still very flawed Comment from : Ben Wearne

Just gotta say, you're videos are awesome Glad they exist Comment from : Jeremy Falcon

So instead of the sample lying somewhere much lower than the true population mean, what if it's lying much higher? Would it be correct to use n+1 instead of n-1 in order to deliberately make the sample variance smaller? Comment from : Sabreen Elzein

After 3 videos, I finally understood this n-1 Basically when we consider a sample from our population and calculate the mean for it, it may or may not be as close to the overall population mean (which is thr mean that matters) so to lower the possibility of a highly distinct sample mean/variance we use n-1 to reach at least near the population mean Comment from : adarsh tiwari

A very interesting and important discussion I made a break in the middle and thought about it by myself I have a rather short explanation: If the sample size n is very small, such as 3, the variance calculated for the sample has more chance to be very different from the actual variance The smaller the n is, the more effect has this '-1' on the result brWhy do we use '-1' and not some other values like '-2', I think it is just a tradition For the smallest sample size of 2, this unbiased variance can still be calculated However, it is not really purely 'unbiased', just relatively 'unbiased' Comment from : sh di

This is not explained at all Comment from : Leo M

But the same can be there for the other end where we would overestimate it? Comment from : Shivay Shakti

Awesome video! Thank you! Comment from : AJ

HibrHow is this S2 variance of sample different from the sigma squared /n formula ( population variance /n) which is also the sample variancebrbrthanks Comment from : MANU PANDIT

Much better than what my school teacher taught me Comment from : DarkTealGlasses

Because of the upper and lower boundaries, samples are biased to be less spread, compared to the population mean, which is typically more centralized Comment from : Arthur Pletcher

What is bogus logickhan academy is jack of all trade,master of none Comment from : Swapnamay Sen

I get the math What I don't get is how you're able to write with the drawing/annotation feature so freakin' nicely?!?!? Either you missed your calling as a steady-handed microsurgeon or there is some sort of stabilization assistance with the program you're using Comment from : scott lomagistro

by this logic it can be n+1 also ig Comment from : Prabhjyot SIngh

8:40 I think you should not represent the true variance and the sample variance on the same number line you drew for the population points Also the consequence of your putting them together is you're visualizing the distance between the sample variance and the population variance on the same number line, resulting in your conclusion that because the sample points are far from the population mean, the variance is far too Ponder over it, you'll realize brLove your lectures BTW 😃 Comment from : Kanishk Vishwakarma

Let's say a report comes out that mentions standard deviation How are we supposed to know which formula was used to calculate that standard deviation Comment from : VGF80

The analogy you’re using is probably not very convincing/intuitive enough Because there’s also a likelihood that the sample is over-estimating the population mean, so why don’t we divide it by n+1? Comment from : liu shao min

This is terrible Still no explanation of why it is unbiased if using n-1 Comment from : Jack

I would like to know why we use the square of the difference between x and xbar, and not the absolute value of the difference? Comment from : john Hendrickson

NOT one of Khan Academy's shining moments You're other video (thanks Dhiraj Budhrani) is MUCH better (with the simulation & a mathematical explanation!) Comment from : MrVpassenheim

Starts at 500 Comment from : Arvin Pillai

9:08 - You are just as likely to be overestimating, you just chose to pick the bottom points rather than the top ones This offers literally NO explanation, let alone an intuitive one, as to why I should expect there to be a downwards bias Comment from : ASomewhatLongAndMeaninglessUserame

So this means that the n-1 of the sample variance equation was just an arbitrarily chosen value because it's empirically closer to the actual population variance? Or is there any equation or a logical path in deriving the n-1? I kinda see that it's the former but kinda feel that there might be a theory that could explain why n-1 is the most appropriate and not any other value and that it's just a natural consequence of our math Anyone who does have one, please tell me!brThank you for the video Khan Academy! It was very informative! Comment from : Jayrald Basan

I can't understand why we would underestimate variance in general this way Let's take population [0, 10, 20] and its sample [0, 20] They have the same mean 10, and variance of the population is (100 + 100 + 0) / 3, while variance of the sample is (100 + 100) / 2, so we overestimate the variance Comment from : imbolc

So I guess the biased variance is better if your sample is still close to the entire population Comment from : ᴠᴧᴨᴛᴧᴃᴌᴧcᴋ

I had the intuition that overestimation and underestimation would compensate each other Why is it not the case? Comment from : Baptiste Roussel

Why isn't this video on the statistics playlist? Comment from : Lucia Breccia

starts at 5:05 Comment from : Alberto Rivero

this does not give an explanation for why it is exactly n-1 Comment from : clancym1

still dont get it yes you would be underestimating it if u take the sample cluster below the mean but if the cluster is above the mean? you would be overestimating it! seems arbitrary to me Comment from : J S

So why minus - 1? Why not - 2 ? Or minus 6,345 ? This is still not an explanation of the n - 1 :-( Comment from : f lotars

Didn't say anything about n-1, misleading title Comment from : Casey

I love you, fuck the rest of explanations on internet, this made me understand Comment from : Upgrad3r

If you want a more technical explanation/proof, Wikipedia Bessel's Correction This video has some good intuition though Comment from : Matthew

Comment from : shahdatyoutube

I GET IT! I had to work out the proof and think about it really hard, but I get it! I have an intuition for why n-1 makes sense! Message me with your questions, because I don't think I can explain it easily in the comment boxes Comment from : Drop Dead Fred

We all hold the key to our part save the world by using and combining knowledge to promote peace throughout the world I'm starting it off as an inventor and entrepreneur Comment from : Archer WhiteDragon

Knowledge is the only hope for world peace We must have save trench town As an actual real world issues that can be mathematically save the world from this little island If you you can do it! Comment from : Archer WhiteDragon

Hey, help me resolve world economics Bringing knowledge Comment from : Archer WhiteDragon

Say there's a population with a known population mean, and you take N random values from it, is there a way to calculate a probability density of deviance of the sample mean from the population mean? I hope that was a coherent question Comment from : Johann Schmidt

Tackle chance variability first Comment from : Blake Shurtz

As n approaches N, s_n approaches sigma, but s_n-1 approaches something that is not sigma So what gives? Comment from : Drop Dead Fred

By the way for anyone curious, the "degrees of freedom" of some statistic, say, a sum across the x's, is n because this number has n ways or parameters (the x's themselves) by which it can vary Using this simple notion of "freedom", you can state the dofs of the any statistic that is written in terms of some data points As another example, the sum across the x's squared also has n dofs Comment from : alkalait

You said that the biased variance was an underestimate, so is it possible to overestimate? Comment from : Euroliite

Perhaps that tends to be overdoing it? Comment from : Euroliite

we cant But we divide by n-1 even if we have 10000 samples, what difference n-1 will make? Comment from : glavgad

I dont get it Yes the error will be smaller, but why we dont divide by n-2, or n-3 or n-4 , etc Comment from : glavgad

Thanks for this video Sal Though intuitive and true, some viewers might find this approach (to dealing with the "bias" in the estimator) heuristic For instance, one might argue "why not n-2 and so on" If you decide to invest a bit more in this stats playlist, I hope you'll get to deeper concepts like degrees of freedom of estimators, which lie at the heart of the concept of this video Please don't take this as criticism; the video is in the right direction :) Comment from : alkalait

thank you so fucking much for this!!! Comment from : Piecakesman

n-1 D: Comment from : WGBraves24

Comment from : Affan

FIRST! Comment from : MrLullumbonum

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