Statistics: Variance of a population | Probability and Statistics | Khan Academy

[@brittothomas8614]

Einstein once said, if you can’t explain a concept to a child, you yourself haven’t understood that well enough. Khan’s academy is an embodiment of what is possible when you understand the concepts through and through.. Einstein would have been so proud. I used to hate Math just coz they wanted me to memorize these without logic. Now I am here in my mid 30s to learn the foundations so as to learn ML and AI. All I can say is, thank you ❤

[@saifurrahman2503]

Wow. I'm here also for the same purpose. 😃

[@jamescameron1665]

Here for the same reason lol

[@IronAceSUB]

Thank you Khan Academy for making this amazing content. You may never see this, but I hope you know that your lectures are worth more than gold, diamonds, and antimatter combined. You have brought free education to millions and inspired the minds of humanity. You give me hope Khan Academy!

[@anjuharidas5864]

Well said.U will go a long way also khan academy for the initiative.

[@major_melatonin4576]

This is my first year in college as a undergraduate, and they stuck me in Probability and Statistics. My teacher isn't the best but these vids keep me going

[@notanape5415]

4 years of the university went by and today is the day I fully understood variance! Thanks Sal

[@joshboston2323]

how were you able to get through university then?

[@notanape5415]

@@joshboston2323 barely did

[@jessefp1940]

You're the only teacher that makes sense man, thanks for your work

[@divakarluffy3773]

awesome thank you sooo much i was really finding difficult in this subject but i am really felling better after seeing your tutorials thanks a lot

[@cmburnsie]

Your videos are very pedagogic! I've posted this to all the people where I work (I'm the only statistician), so perhaps they can understand what the variance is for once =)

[@Peter_1986]

Sal has realized that teaching is all about explaining things until there is nothing left that needs explaining. He doesn't just go like "okay this is how it is, do this step now for some reason, because that's how it should be", he actually takes the time to explain in-depth.

[@kimshank-o7n]

This is saving my life in online math, they don't give you ANY resources.

[@1980futureclone]

THANK YOU! I'm taking GIS470(STATS for geo.) with a recent grad that has no idea how to teach. I've learned much more from your videos than his boring, uninspired lectures!

[@xt.7933]

In my 40s', watching this because I am working on a Data Science degree. Not sure if Khan will help me learn better than 20 years ago when I was in college.

[@thomsondcruz]

Hey Sal, typically when the sample mean is calculated, it is the sum of all the values divided by (n-1). The reason we use n-1 rather than n is so that the sample variance will be what is called an unbiased estimator of the population variance.

[@TheAlbatro55]

omg... these whole video list are so addictive, I can't stop watching them!

[@sundusnasir]

is it sad that I am in my fourth year at the university of toronto and I am using this to help me in stats. shame on my prof.

[@TheDukeanator414]

In in the same predicament right now. Failed stats at San Diego State 4 years ago, don't remember anything, now trying to relearn for my upper level course at FIT

[@bellatrix9256]

so did you graduate?

[@bigman6845]

shame on you lol, should have put effort earlier

[@aungzawnyein3198]

@@bellatrix9256 Haa

[@user-uv7bk5rk2c]

@@bellatrix9256 he didn’t make it

[@VV-zb7pm]

Thank you! And voice is like butter! Can listen forever

[@AlexSmith-tr9hc]

@Taha Shah It just looks like 2-1, but his writing is small and hard to read. It's still i=1, not 2-1.

[@zararedwood8400]

very helpful videos sir please start videos for the cfa course also I'm sure it will be very helpful to all the cfa students worldwide appreciate your work very enlightening videos

[@Athenaman717]

Love ur vids man...i am taking a business stats class after many years of stat 1 and 2 and this is a good easy to grasp refreshal

[@ItalianM0bst3r]

LIFE SAVER! I have a stats prof. who has a strong accent who i literally can't understand at all. Thanks to you i am learning !

[@revysingh]

I believe the equation for the sample mean is incorrect. you do not divide by small "n". You divide the sum of the total sample values by "n-1". It is important to divide by "n-1" in a sample mean. That one characteristic differentiates population and sample mean. A sample mean is an estimate of the population mean, and thus the "n-1" helps make the mean a sample of the population mean.

[@kyh6767]

that shit is explained in the next vid

[@MaryamNiazii]

You should kindly correct the mistake in the previous video. Or mention in the end, for people who only intended to watch that particular topic. :)

[@محمدفتحي-ذ9ر2ض]

I don't think it's a big mistake to correct they're just variables. You can name it n, i or even Maryam Niazi.

[@industrialdonut7681]

yeah it's hardly even a mistake

[@AdeleidaBingham]

Around 7:43: x4 = 3 (you say 4 by accident). Brilliant video, as always, thank you....

[@efisgpr]

as i understand it, there are two ways to make something positive; take the absolute value or square it. they chose to square it. of course, u can just use standard deviation (square rt of the variance) if you want a measure of spread/dispersion that uses the same units as your data pts. :)

[@MegaWeirdchild]

I have a question. See if these numbers (2,2,3,3 and 0,0,5,5) were each on separate tetrahedral dice and you rolled them together, which one would have the greatest probability of winning and how would you work that one? Would variance be taken into account?

[@trentonhord4919]

+Human Person It would be a question of odds calculated using probability. Variance would not be used.

[@misajohncarlo4449]

thankyou. Ihave a question...my teacher told me that you need to subtract that N=4 to 1 in getting the variance part

[@misajohncarlo4449]

that's xi - mean/ 4 - 1 to get the variance. ;)

[@kristietwining5597]

So Awesome! It makes stats fun!-almost

[@julesthe13]

Will you make a covariance video? These are really great. They help more than my books and my professor.

[@BeanSprouts02]

Is the square on that difference between the values and the average all for the purpose of making them positive values? If so, why is there no operation of doing the square root for them? Because if they’re squared, then that means the value is doubled, right? Thanks for the video!!

[@xbuchtak]

@josenros I'm no mathematician, but I think it's because the properties of the sum-of-the-squares function, the sum-of-abs-dif func is non-linear, causing some problems not to have closed formula solution. Actually the formula for sample variance sum((xi-mean)^2)/n can be derived as a maximum likelihood estimation of population var., meaning that the calculated value is "most likely" close to the correct value under the assumption that the numbers xi follow the Gaussian distribution.

[@omgu8mynewt]

Thank you for explaining this to me, I didn't understand at all from lectures and the textbook (yr 2 biologist at uni). You're right, it is very easy when you follow through the equations, lecturers just show the equations leaving us looking blankly at them.

[@kandevie]

Statistics simplified. Good to learn.

[@jakewilson4301]

Thanks for these videos. My stats textbooks are fine, but these are more succinct and comprehensible. My psych degree is a breeze now. Kudos!

[@tharaki0kurt]

Absolute values are not that easy to manipulate 'algebraically'. Squares have been used as acceptable substitute for the 'absolute operator/function' throughout maths and physics. PS:- If you have to write an absolute function in terms of 'basic' operators, it goes something like this. ABS(x)={x: if x is greater than or equal to zero OR -x: if x is less than zero}. So any further operation you do will have to take these cases. You see why this would get complicated. Hope this helps.

[@ManiacallySmithing]

Pretty good tutorial, terrible greek letters. Thank you for this, man. I'm teaching myself math all over, as I never quite got it. You're a great big help.

[@SAmanteaColls]

Can anyone give an intuitive explanation for why we're interested in the average square distance from the mean and not simply the average distance from the mean? I get that it gives you a positive number but we could just as well have used an absolute as stated in the video.

[@022samuelabraham2]

Thank you so much.

[@beto1glez]

YOU ARE MY HERO!!!!

[@Kurgipurk]

At this point, its 3am. I'm kinda sleepy, but not sleepy enough to get off of youtube. I find this so fun to learn that i got my notebook out and started writing this stuff down. Talk about an excellent teacher... :P

[@user-cv2se6mh5v]

Wouldn't it make more sense to calculate how much, on an average (mean), every data point diverges from the mean? That way the data points of the set {0, 0, 5, 5} would on average (mean) diverge by 2.5 from the mean which gives you an understanding of how spread of the numbers are. What is the point of squaring? You could just take the abs-value if you want positive numbers.

[@hasanboyyuldoshboev1124]

DEAR TEACHER ! COULD YOU PLEASE GIVE MORE EXAMPLES WITH NUMBERS? BECAUSE YOU HAD EXAMPLES IN PREVIOUS VIDEOS. REALLY REALLY THANKFUL FOR VIDEOS))

[@pedantic_academy]

Legendary Salman!

[@EinstienJr]

same here. and i cannot just mug up formulas man. And Sal SD explanation is the best ever

[@samii2594]

Just wow!

[@melvinlijiabraham4165]

Can't variance be over-estimated as well, as in case if we took data points to the right? So, in that case, we might need to divide the sum by "n + 1"...??

[@kandagatlapavanikandagatla3841]

THANK YOU SIR

[@tharaki0kurt]

It has to be squared so as to get a magnitude of the difference and not the sign. You could have taken the modulus but I guess the guys thought that square was just easier to work around with for later results.

[@tharaki0kurt]

In easy terms, if you just add the difference of each data from the mean you would get zero as the result. Visualise this. Mean would be right in the center of your data points. Right?? If you take the sum of the distances of each point from the mean, because the mean is in the center, you would have as much distance (of the points on the left hand side) as you would have on the Right Hand Side. Hence their sum would come to zero. Hope this helps.

[@abhishekdeshmukh1704]

thank you

[@Nerrrddi]

okay.. I was taught that the denominator of the sample isn't just "n". It's "n-1". The population denominator remains only "n". Am I wrong?

[@hyelimsong5171]

+Priscilla Mosby I was taught the same way! We use "n-1" as the denominator in order to minimize the error.

[@Nerrrddi]

Glad I'm not the only one who noticed that!

[@vineethmenon5546]

When you consider the whole population, the denominator is N as in this example

[@mMorgan359]

that applies to the variance of the sample not the variance of the population

[@ksoflyineer]

Watching this makes me realize how much my professor is flat out terrible, no offense since he's a super cool guy and all. Something that takes him 2 weeks to explain, you are able to convey and teach in 12 minutes. Thank you so much!! :)

[@otissumnerbrown]

I like this - the clarification is a big help to me.

[@smitshah415]

this very help full to me..........

[@nagevaaa8199]

i have a statistic exam within 2,5 weeks...so iam gonna watch al these khan videos oh yeahh :). Dis gun be gud

[@marshwiggleme]

I got confused after the other video with the introduction of i. Now I dont know what is going on.

[@Peter_1986]

Anything is manageable if the teacher is good. Math is infamous for being "boring" and "complicated", but Sal proves over and over again that it's actually very straight-forward and can be very fun - he even manages to include absolute values in first-grade lessons and builds up to matrices and complex numbers as if it were nothing special, lol.

[@alokmishra5638]

Brilliant Video Thanks a lot sir

[@346rrr]

I'm lost. Does anyone know a better channel that caters to statistics for beginners. Please recommend.

[@junmarkz]

Thank you so much you save my whole sem of GEC

[@iamb2348]

So whats the difference between a variance of a population and the standard deviation of a population?

[@iamb2348]

Anon Ymous Standard deviation is the square root of the variance. Thanks google

[@LeoAugustom]

Shouldn't the square of a difference be determined through a^2-2(a.b)+b^2???

[@bobichina]

Thanks a lot. You are great

[@paulceltics]

thanks

[@pierce3992]

“Let me show you what I...MEAN” 😭

[@neemakalumia]

😂😂

[@MrUnix-xf8dq]

I thought the same thing lmao

[@1979akak]

Ok

[@tharaki0kurt]

My point is that variance is difficult to visualize in your head. 'VAR2' ( defined in my previous comment) is easier to define, visualize and understand. But its not used because of the associated calculation issues. PS:- I am not an authority on the subject. Even if I was, questions like these are still being debated. I hope this explanation helps.

[@10bengy]

I think that these lectures should be arranged in sequences because, it is easy for someone to lose track of what the next lecture is going to be.

[@dinamarwan5735]

hello there i need help by solving this problem if we have a x,y,z with a variance of 2 what is the variance of ((-z/z+3),(-y/2+3),(-zl2+3) so could u find the variance ??????????

[@heymavis]

i = 1 this refers to the i in x sub i, this means u start at the data point where x = 1, the first data point

[@Ucsd4life]

I'm just thankful for this FREE help

[@Inspiteofallthedanger]

It seems more intuitive to me to take the absolute values of (Xi - mean), and then find the average by dividing by n. Why do we square the difference instead of just looking at the magnitude of the difference?

[@lhyx1990]

which software r u using? it's funky!!

[@littleAlex44]

i dont know how to thank you. thank you

[@SuperNation22]

this is amazing how do you profession in area of academics? really everything i watch from you is as though you master in that part alone

[@aqilraza]

you are amazing Sal.

[@andrewnickell5516]

Isn’t the sample mean divided by n-1 ?

[@MrCalhoun556]

So you basically say absolute values are more exact but not used since the modification of formulas considering absolute values is much more difficult?

[@UndefinableGaming]

@10bengy try to going to his website, they are in order there.

[@tahamohannad8528]

This always confuses me. When he writes the Sum symbol and the N ontop of it and all that jazz, what does he put under the sum symbol? In the first vid, he put an i=1 now he's putting a 2-1? pls halp

[@milanstevic8424]

there is no 2 - 1, only i = 1, it's just blurry

[@GeorgeCopperfield]

Okay I'm glad cause this was frustrating me so bad. Bad handwriting is my biggest pet peeve

[@meghaarya78]

Sir where should we do exercise ????

[@coolygirl9]

Sal is a life saver

[@RossRocks07]

thanks!! helped me so much!

[@EinstienJr]

in case of grouped, ungrouped data etc............and all other data???

[@deadboy000]

hey mr. khan, i wished u used a computer with handwriting recognition which would be much easier for u and for us. thankx

[@thisdayaccount406]

WHY HAVENT TAKEN MODULUS RATHER THAN OF SQUARE ?

[@sonam5054]

Superb video! Thank you so much!! :)

[@tombrady7390]

shouldnt there be small n in the formula for deviaition instead of N

[@nrsnia2007]

I dont know who you are.... but I think I love you! You !

[@Inspiteofallthedanger]

Ah, I understand. taking the average of the absolute values would give you the absolute deviation. The variance is a squared deviation, by definition. I'm still not so sure why in what cases it would be more useful than the absolute deviation.

[@terryn9450]

wait why are u dividing by the number of the data? is this variance different from the one and probability?

[@IRAETADELAPAZ]

under that sign you have the N on top and whats on the bottom i can't clearly understand it. I'm just trying to write stuff down for future reference.

[@MrFarkasOfficial]

Epic Khan is epic.

[@jwise6405]

gets confusing when teaching the regression parr and plugging in the numbers in each column. Not taking it step by step and showing you what's being added or subtracted or squared( #s)

[@ramxx]

GOD BLESS YOU.

[@corradoblondi9792]

nice

[@jameslee3508]

What does the 'i=1' mean?

[@SagarGuhe]

That is way to tell that you need to start from first value that is x1...

[@zeeshan3dge]

love your "I don't know"

[@sam4395]

Thank you so much Sal :')

[@SagarGuhe]

Can we say that population mean is kinda calculated on the real time data? And sample mean on sample data may be based out on a survey data for instance...

[@loudspeaker237]

i need a formula that has the current population adds the births and subtracts the deaths.

[@xbuchtak]

@josenros I'm sure this sounds a little bit confusing, just watch more Sal's videos or look the details up on wikipedia. It'll come together ;-)

[@AnastasiaPywell]

variance is using N-1 not just over N...