Statistics: Alternate variance formulas | Probability and Statistics | Khan Academy

[@darbylane]

why am i paying tuition that goes to my professors when I'm always watching your videos. Literally every class. Physics, Biology, Statistics... You're saving my life lol

[@dilbar09naz]

+Amanda Darby because professors are not really there to teach, their actual job is to do research but they also teach on the side, they don't have an education degree. but Sal teaches better than majority of high school teachers who have education degrees :/

[@blownspeakersss]

+Slacker1221 That's not how it works. Virtually no professors have education degrees. As the previous person said, professors are supposed to be experts in their fields--not "teachers" per se. Like, at university, an actual economist (whose job it is to do academic research) will teach you economics, not an economics teacher. Ditto with any other subject.

[@jeffconway8729]

Yea, ironic that college costs increase when you can get at least 60 percent of your knowledge from the Internet, probably more. College costs should be going DOWN, not up. what a racket!

[@blownspeakersss]

The availability of information on the internet is pretty much unrelated to college costs.

[@brianm.4368]

Yet Sal's opposition's best attack on khan's credibility is that they disagree with his definition of slope. Khan Academy, The Organic Chemistry Tutor, mathbff, and patrickjmt can literally fetch you a 3.9 to 4.0 gpa (university), unlike their live counterparts.

[@tusharagarwal2040]

Omgg, and most teachers and other KZbinrs too just give up at this point and simply say yeah this is the formula just remember. But after doing statistics for 3 years, finally I know that this is how it's derivedd. Oh God the satisfaction, thank you so much!

[@bloomingelegant590]

finally, someone has given me hope for statistics

[@KirtiDwivedi-q1m]

So what are you doing at present

[@shadosavage7755]

This one was somewhat tough to absorb, but I'm loving this course. I feel like I'm learning exponentially faster than I ever did in school/college.

[@PerceeP927]

this whole thing is mewtwo! 7:56

[@samuel94city]

Dude you are amazing. This was actually funny. Pokemon Fan!

[@belzhang5745]

Samuel Augustin plus one🙋

[@whitec1981]

where were you when i was bombing stats class in 2001-2002 Ha ha man has education come a long way!!!!

[@bigrobbyd.6805]

Dude! That is amazing. Thanks for the help!

[@mouradbarakat123]

Thank you Sal. You are driving colleges out of business :)

[@jakereason8095]

Note that the derived forms will only work for calculating population variance and not sample variance since you wouldn't be able to substitute the arithmetic mean one of the expanded polynomial terms; I had to learn this the hard way.

[@nitinraturi6374]

Jake Reason this will work with both sample and population variance. You just have to derive the formula for sample variance just like he did in the video.

[@Ihatenicknames1]

This is very helpfull, I watched all the statistics videos and love the topic now Thank you so much, you have no idea how much you have helped me

[@koby9340]

did you graduated by now xD ?

[@Ihatenicknames1]

@@koby9340 hahaha yes! I work as a software engineer now and am very happy with the job :D

[@koby9340]

@@Ihatenicknames1 Congrats man so happy for you

[@alenjose3903]

10 years. Feels strange.

[@nocturnalvisionmusic]

@@Ihatenicknames1 that's nice man congrats :)

[@shazaduh]

The standard formula requires that all of the samples be involved in each new calculation. This is a very inefficient use of computational power and memory, but with above formula, running tally is kept while moving through the signal. This is good for microprocessor or FPGA in DSP design.

[@orpheus1664]

I highly reccommend this guys videos, he's VERY good at explaining things simply, which is not easy when stats is concerned :-D

[@Czathero]

You are now officially my review for my Stats class.

[@aknavychic2234]

I love these videos....they are soooo much help! THANK YOU!!!!

[@soumyonayak]

Exactly the video I was searching for.

[@konopong]

mu squared times the sum of ones in the numerator comes from the fact that you add mu squared N times, which is simply Nmu**2. After you square the original variance numerator you need to sum each of the three terms from 1 to N. Hope this helps.

[@MrNicorodriguezD]

I've got a question... If I have the size of the population, but I just need the variance of a sample, e.g: (N=60, n=10), then I should use n-1? thnx!:)

[@mapa5000]

Fantastic !!! Thank you

[@THE16THPHANTOM]

@SuperRockstar206 doesn't matter how young you are you can do this if you can add,subtract, divide and multiply, and watch the play list. long live you-tube...and this guy that does this.

[@karabaines5918]

I sat through so many lectures last year trying to understand all this stuff and this guy has made it sooo easy !! Thank you !!!

[@miamirealestatetube]

thank you!

[@haappyone]

noone else can teach like you . You are a great teacher. keep it up. It's really suprising to see three dislikes for this video.

[@GabrielConstantinides]

Thank you for such an amazing video, really well explained.

[@tusharmodi9883]

I don't understand the intention of making this video the concept of variance was pretty much clear in last video and this video had confused me more. so keep it simple and straightforward

[@amber1862]

tushar modi You've probably figured it out by now, but just in case someone's reading this and thinking the same; a lot of statistics is done algorithmically using computers, so working out the variance with the new ways presented in this video could potentially reduce the time it takes to calculate the variance with a computer, and if you're dealing with a huge amount of data, that's significant. When you write computer code, sometimes you have to write more 'messy' code upfront to actually force the computer to perform less calculations by doing it in the exact order you told it to, making the program more efficient. Computers don't care about messy code, all they care about is instructions and the order of said instructions.

[@tamaleseason]

oh thank you so much!!!!!!seriously i have a stats final in 7 hours and you helped me out so much thank you!!!you make it so easy!

[@alenjose3903]

did u pass?

[@chetankv7218]

Hi, I have tried to still deduce variance formula, however seems i am seeing there is an issue in this deduction. Could you please help me understand it Currently we have below equation variance= sum(xi)^2/N - mean^2 what i did was for the first part sum(xi)^2/N i multiplied and divide by 'N', so it looked something like below: N*sum(xi)^2/N^2 --> N* (sum(xi)/N)^2 --> sum(xi)/N is mean formula So, Variance = (N* mean^2) - mean^2 --> i took mean^2 as a common term Variance = (N-1) mean^2 --> this formula seems to be not giving the result i want

[@LegoEddy]

Hey, I hope this answer still helps you out: You have to watch out whether you compute sum(xi^2) or sum(xi)^2, because they are not the same. That means that you have to start with variance= sum(xi^2)/N - mean^2, and then you will not be able to transform the first term into the mean formula.

[@wally9y9]

thanks, i know it right now which i dont understand woth my statistics's notes.

[@lorenasiu3113]

Thank you so much, I hate learning formulas without understanding

[@cheesiechess3656]

But I have even more formulas for the variance which is confusing. I have unbiased estimate of population variance: (N-1)/N * s^2. And I also have the: Unbiased estimate of Var(X (bar)) = s^2/n (1-n/N). My problem is mainly that I don't understand what Var(X bar) means (I cannot write a bar over X on youtube comment).

[@rewindvampire66]

I think I like the other way more because this one was a little harder for me to grasp

[@lattethebunbun]

sorry to bother!! I am wondering why when you facetored out mew squared it is left with a 1 in there? thank you!!

[@bigcheesetaste]

beautifully explained!

[@niranjanchakrabhavi8601]

While writing the equation of variance, please divide the term by N as soon as you write the numerator. It's annoying to see the denominator left out.

[@manfredmichael_3ia097]

Its 1 am, and 8:00 opened my eyes!

[@Gruemoth]

the pixel quality becomes so banal due to the colors and the simplicity of the explanation. Math is beautiful

[@ninjajesus81]

@yynotx I still don't understand why the third sigma term is multiplied times 1. Why would that cause the moo to become it's coefficient? And if you're multiplying it by 1, why even put the 1 there?

[@bahareomrani1039]

amazing video, may I ask you what is your software? thanks

[@nabildatascience7422]

love you khan good explanation

[@PressStartLetsPlay]

This guys a genius.

[@shivamchoudhary1681]

Can we do the same thing for sample Variance?

[@rebel7332]

Thanx, I like your way of teaching

[@aozcakir2]

watched on Jan 04, Thanks

[@ezramagiya8581]

Wow it is indeed helpful

[@piyushmajgawali1611]

mean of squares - square of mean

[@itubie]

There is a random variable X with its mean 10. Moreover, we learn that the mean of X^2 is 26. What is standard deviation of this random variable?

[@junmarkz]

Just square root the variance to get the standard deviation

[@chandraveersinghsolanki8371]

this is the tutor I’ve been taught by

[@MatmarSpace]

The video may be 240p but it explains the topic in 4K.

[@chaosui3169]

This tells var(x)=E[x^2]-E[x]^2

[@DogeMcShiba]

Indeed. To anyone reading this, E[x] is called the "expected value" of a sample/population, which is pretty much the equivalent of the mean. It's essentially just a shorter way of writing it instead of all the Sigma signs and such, since you can write e.g. E[x^2] which is the mean of the data points squared.

[@FakeMath3000]

But wheres the divisor (N and N^2) though?

[@UltraRik]

7:58 This whole thing is MewTwo

[@krishhsingh4034]

copy -_-

[@UltraRik]

huh seems like a lot of people heard the same pun

[@jijie133]

very good.

[@backstudy27]

This is beacause the sigma applied to everything inside the brackets, including the constant u. (u is a constant because there is no x-sub-i to contribute to the sum).

[@MrJonPala]

Would sample variance end in a (n-1)squared?

[@MrsIssy2010]

Omg I love this. Thank you

[@Enviousful]

Shouldn't also been ... -2*u divided by N + u ..., because it is the whole formula divided by N? Hoping an answer

[@mrcool4uall]

Can anyone comment on this please? Even I have the same doubt.

[@SpacedFiction]

Mew and Mew 2. Gotta catch em all.

[@imaginaryunit.]

7:58 Mewtwo! :D

[@DiogoQNT]

LOVE YOU BRO!!

[@dfsfklsj]

Ahhh!!! I totally see it now! How can I forget to look at the sigma sign! Anyway, thanks for correcting me, I'm a freshman in high school so... :P

[@yalnayal]

mindblown

[@sarveshingale]

thanks

[@Carlosenzone]

mewtwo

[@davialbuquerque4964]

Have you already watched the new Pokemon movie?

[@krishhsingh4034]

hol' up

[@LearningTheBasics001]

seriously you will be writing my final exam for me

[@ConnieWEN-0512]

amazing！is it magic? no it is maths!

[@garlicgirl3149]

For a second I thought you were speaking a foreign language then you redeemed yourself in the end.

[@frenchmike]

0:07

[@dman22180]

No he didn't; he simplified it from Sum(M^2) from i=1 to N, which (from summation rules) he brings out the constant to the front so: M^2*Sum(1) from i = 1, to N. Sum(1) from i=1 to N is just N (you have N 1s). So you get M^2*N/N ==> M^2

[@jamesleem.d.7442]

At 12:13 check how you pronounce the verb "iterate". "Eye-Ter-Ate" ? I don't think so.

[@zakariaibrahim6781]

Why do you divide by N not N-1???

[@Ryan라이언]

why is mu^2sigma 1 to N = mu^2 N? and not mu^2? can some one explain it for me :(

[@THE16THPHANTOM]

big boy mathematics. (i think a kid in primary school can do this if they watched these videos.)

[@InMooseWeTrust]

What is the point of doing this? I was confused enough with the standard formula.

[@tautologicalnickname]

7/59 MEWTWO!! XD

[@kariakichernocherno2274]

The formula looks more easier

[@frito94791]

Mewtwo 7:58

[@dfsfklsj]

Ummmm. M^2 is a constant, and it is totally inllegal to time it by N. The final formula should be m^2/n instead of m^2. I think you made a big mistake!

[@alyaasaad433]

👍🏻

[@Sonnett7]

Pokemon fans - check out 7:59

[@jimmyzsan8702]

SS = sigma x^2 -( sigma x)/ N. sigma ^2= SS/N this is easier, yours seems wrong from those multiple methods

[@jamesmclean8751]

You were purely flexing in the video.

[@lovedog49507]

This stuff makes my head hurt.

[@VleerLab]

lol that's what I was thinking

[@adbasdbasdkasdja7246]

awesome but really shitty quality.

[@shekelboi]

And what am I supposed to do with the last equation? 💀

[@MrFernandoBedoya]

I have the same question. I think he make a mistake.

[@gopalb167]

I love you na raja

[@deadboy000]

i failed on statistics -.-" lol

[@mayuri3964]

So confusing 😞

[@sulandelemere]

I was doing good until I hit this video which just confused me. Maybe have to come back to this later. I think too much is assumed of the learner in this one.

[@joshboston2323]

I agree

[@catalinagonzalez3635]

you just lost me

[@MissDJ]

i hate numbers