Statistics: Variance of a Population

[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.

[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

[ydym30]

You do have a way for teaching. Thx.

[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

[JackAttack363]

Said 4 wrote 3. DOH! >.<

[x3triLogyx3]

you are absolutely amazing.

[josenros]

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.

[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.

[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 ;-)

[josenros]

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?

[ellemheaven]

wow this is amazing..thank u 

[tangerinetigerr]

thanks so much for the black chalkboard background; i am almost legally

blind, and white w00d be to0 painful to l00k at; i use black backgrounds

all over my pc, whether notepad, word, or firefox!

M-80811...1217AM

[beto1glez]

YOU ARE MY HERO!!!!



[Carebearbull]

haha I rofled at 05:21

[888phoenixx]

@Carebearbull me too i nearly started writing big sigmas

[cyrubio]

thank goodness for khanacademy!

[paulceltics]

thanks

[cleverlocs813]

I have this packet due the day i go back to school from spring break and i had forgotten the examples my teacher showed me but i was intellegent enough to actually realize we are living in modern times and technology is a big help so is youtube..lol

Thanks and i give my appreciation for taking the time to help those like me on some real shittttt..xD

[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.

[pstaff716]

thank you very much

[DawnBreaker1100]

Who dislikes this stuff??

[TheGameCollection]

@DawnBreaker1100 jealous maths tutors

[JLchevz]

What Sal is doing, is making our lifes better.

[pinesolparrot]

you are truly making a difference in the world..we can all be smarter now ! thank u so much !!!!!!

[julesthe13]

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

[tomrox1523]

i have recieved 2 messages about my past comment. i want to clear this and say that was a friend. im not one to argue. it's a waste of time. EVEN MORE on youtube with strangers

[bobichina]

Thanks a lot. You are great

[tomrox1523]

your gay y wud u put this on utube

[fplusk]

@tomrox1523 because he gets paid millions for it you idiot !

He is a youtube partner that is educating the world (clearly apart from you) for free

[MyBloodyQuarantine]

144 likes, 0 dislikes. i go to my email: 144 unread messages, 0 spam. is the world ending?????

[Mr46ser]

this is amazing. I regulary fall asleep over my textbook and in my statistics lessons. But with these videos, i can't stop watching. Thanks a lot!

[nazirdjon]

SAL i love you!!!!

[loudspeaker237]

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

[28kb]

lol x sub 4 = 4 but u write 3

[SuperhumanChichi]

@28kb

He wrote it correctly, it is 3, but he just says it wrong (he said 4)

[deadboy000]

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

[3runrob]

if you wanna know how many videos youtube has or many other facts about youtube click on my channel

[ramxx]

GOD BLESS YOU.

[blaznsnow]

it is hard to read your handwriting x]

[Guitarist2098]

@blaznsnow thats not his handwriting thats his mouse pointing "_", his later vids it looks like he has a digital pad or something cause its his actual handwriting.

[pan02286]

unnecessary mention....I just 'heard' , x4 =4.good video : ]

[coolygirl9]

Sal is a life saver

[sumitece87]

Truely Excellent.... Thanks Sal

[aozcakir2]

watched on 2009-12-30

nice

[yynotx]

watched this to take a break from the linear algebra videos--another excellent video--i wonder

i you have a master plan or do videos as things

pique you interest--clearly the lin alg section was

pretty planned out

[Jakers2009]

What???

[77sallu77]

AMEN! I I  I v

[isthatmylita]

not sure why, but Sal, you have some kind of magic and I'm beginning to get it, exam is in 3 days, a little late maybe, hopefully I can still pass Stats, thank you so much! I still need to get correlation and regression, so if you have any spare time in the next 72 hours....its ok....thanks again

[cusanusnicolas]

If you've done randomized blocks you should enjoy my proof for an r value for blocks that indicates orientation to an external gradient. The vid is a layman's explanation, but the website has the detailed proof.

[BurningBright4ever]

I've always wondered why the difference between the mean and xi is squared. Does this have a particular purpose? Why does it have to be squared why not just take the difference and divided it by N and leave the sqauring of the numbers out of the equation

[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. :)

[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.

[BurningBright4ever]

well then why not just use absolute values? The variance would then  be much easier to visualize in terms of the data.

[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.

[MrCalhoun]

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

[tharaki0kurt]

"exact" would not be the correct word here. Variance is a measure of dispersion of data about the mean. That is that. It gives "a measure" of the average distance data points are from mean, but not the average distance itself. Now we can define another value, say VAR2 that is defined as the mean of distances of data points from the mean. Here the absolute value would be used and . That would be a measure of dispersion as well. 'Perhaps' a better measure.

[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.

[Zetapoo]

Hi there, the reason that squared errors are generally used instead of absolute values of the errors is because of convenience. Squares can easily be differentiated, this leads to many important results in statistics that are derived from calculus without having to worry about points where the derivative does not exist(as is the case with absolute value)

[ahsimpleman]

Do you do any Analytical Chemistry ???

[02280228]

look at khanacademy (dot) org

[jceja24]

whats the numbers / letters under the greek letter E? 2-1 ??

[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

[psyduck1155]

I wish you were my teacher!!! Thanks for this

[lhyx1990]

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

[sweetascandy1302]

isn't the sample variance sume of all (xi-x)^2 over n-1????

[sweetascandy1302]

oops nvm lol

[nrsnia2007]

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

[ckulis]

You Saved my Life. I pay $2,000 for summer classes and $200 for a text book and at the end of the day this is the only way i learned this stuff. Thank you.

[havlatking]

@ckulis i agree 100000000000000%

[k1koth3gre4t]

@ckulis you must be american

[moorm2008]

thank you very much Salman

[dergadude]

this helps with my FST course alot

[keeplearn]

Your explanation is awesome ^_^

[keeplearn]

Thank you Sal for posting the statistics part. It is very very very useful! THANKS A LOT!

[crislangpo]

youre right...

[bradkey98765]

err what? you hat someone and you hop... what???

[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 =)