Standard Deviation and Variance Explained Statistics Class

[5COTTx]

when do we use variance in real life? how does a number squared help us? and not just use the standard deviation?

[Scotthawki]

but why is it n-1 to begin with? What's the relevance, or why do we subtract 1 from the sample size? rather than just dividing by n ?

[statisticsfun]

@Scotthawki wow, that is a great question without an easy answer. It has to do with a correction of sample that is potentially biased.

Another way to think about it is If we have a sample of just 1, with n-1 the standard deviation = undefined. Which makes sense, but if we don't subtract 1 then the standard deviation = mean which does not make sense.

This French guy thought this up and his name was Friedrich Bessel (may have been Daniel Bernoulli).

Make better sense now?

[statisticsfun]

@statisticsfun oops... not that it really matters but Bessel was a German mathematician not French.

[Scotthawki]

Why is the denominator n - 1? and not just n ?

[statisticsfun]

@Scotthawki n-1 is used for samples and n is population. Notice as n (sample) size gets large the n-1 does not make a lot of difference.

[04lewzale]

beast explantion 

[pinksnowbeach]

Why does my textbook have the denominator as N and not N-1 in the Variance equation?



[statisticsfun]

@pinksnowbeach Great question, n is for a population and n-1 is for a sample, sooooo... you are more than likely looking at the equation for a population. Also, as the sample gets large the n-1 part becomes less important.

I probably should have been more clear in my explanation in the video and compared and contrasted t n and n-1 -- oh well something to add in another video.

[pinksnowbeach]

@statisticsfun Thank you so much! Yeah, I am in statistics for social sciences, so that is why. Had I read the rest of the chapter I wouldn't have panicked. But, oh well, the explanation is much appreciated!!!

[brewsie2]

what does the E stand for in the equation?

[statisticsfun]

@brewsie2 The is called "sigma" it means to sum up or add it all together. I should have defined that symbol too.

[123datta123sai123]

thanks a lot, i have a test today and it was really helpful!

[MiiNDLeSSMight]

thanks i have a test today

[statisticsfun]

@MiiNDLeSSMight Good luck! and please let me know how you do on your test.

[MiiNDLeSSMight]

@statisticsfun I aced it thanks a bunch!

[statisticsfun]

@MiiNDLeSSMight "holy schnikes you passed"... great to hear you aced it.

[MiiNDLeSSMight]

@statisticsfun 105% perfect score, highest in the class :D

[statisticsfun]

@MiiNDLeSSMight Wow that is great!

[cronnin]

But you have 6 samples, why not divide it by 6 to get standard error?

[ampadde]

what is the difference between the standard deviation and the variance?

[statisticsfun]

@ampadde The standard deviation is the square root of the variance. The standard deviation is in the same units as the mean to (which is important).

For example if the mean distance is in miles then the standard deviation is also in miles BUT the variance would be in miles squared. I peter standard deviation because it is in the same units and easily compared with the mean.

[kc243243]

wow the best math video i have ever watch, i am more then willing to pay, and if i do pay i will tip as well. i am very amazed!!!!

[abhishaikkumar9]

The explanation was amazing if I would have had a math teacher like him I would have had a better score

[feynmanrichardp]

Thanks,very helpful! Like it.

[SuperStevenHarper]

This was the most helpful video on the web. Thank you for explaining it perfectly :)

[DahniSmith]

The mean of 10 numbers is 8. If an 11th number is now included in the results, the mean becomes 9. What is the value of the 11th number? Produce an algebraic solution. How is this a standard deviation / variance question? and how would I go about solving it? I don't have any values to use, but my teacher claims is to do with the mean and standard deviation, I just don't see it! the question or what i am supposed to do!

[statisticsfun]

@DahniSmith this is a great question. The formula for a mean =  sum of all the numbers / n (where n = sample size) also n times mean = sum

if the mean = 8 and n = 10 then the sum of all the numbers is 80 (10 times 8). Now if you add one more number to the sample the sample size becomes 11 and mean is 9, so the sum = 99 (11 times 9). You can determine the 11th number by 99 - 89 = 19. The 11th number is 19.

(80 + x) /11= 99 and x = 19 (where x is the 11th number).

R u good to go?

[DahniSmith]

@statisticsfun I am good to go =D thankyou so much =D I understand it perfectly!

[ramgon254]

If you tell me where you teach, I'll just take your classes instead of the ones from my rocket scientist prof. Thank you for this. You have great patience and speak English, not stats. The fact that you "interpret" what we're trying to find, or what the final answer is, is very helpful. Thanks, again.

[statisticsfun]

@ramgon254 Yes, this is not rocket science! Thanks for the comments much appreciated. I am always looking for ideas for new videos, so let me know if there is anything else you would like to see a video of.

[ZelenaZmija]

i'm preparing for a test nd i haven't been exactly paying attention in class so thanx for the great review.

[TransientWriting]

this was very helpful, im preparing for a test. thank you very much!

[gratefuldead1112]

My question is what does the Sample Standard Deviation, 5.76, signify? What does it tell you about any given random variable?

[statisticsfun]

@gratefuldead1112 The standard deviation measures the "average" distance from the calculated mean. The mean is the "average" distance from 0. The standard deviation is in the same units as the mean. The larger the standard deviation the more dispersed the observations.

z score is standard deviations. If you calculate the z score it tells you how many standard deviations (how far) the specific observations is from the mean.

[gratefuldead1112]

My question is what does the Sample Standard Deviation, 5.76, signify? What does it tell you about any given random variable?

[Camste85]

Thank you so much for this video! This taught me what my stats. professor confused the whole class about last week! I actually get it now!!!!

[georgiareppin]

Good video. Writing everything out may take time but it's well worth it. The slower the better. Thanks!

[EFFAYBEE]

This video took only 5.05 minutes to THOROUGHLY teach me what I failed to understand in a full term. Thanks !

[allchangesintime]

very nice, thanks for this :)

[curiosityplease]

thanks so much! this helped me out with my statistics project :)

[latterthought1]

This was better explained than ever before in my years at a very prestigious private school...

[moguai352]

So cool! I appreciate your help a lot! :)

[moguai352]

I try to understand what for the Variance is calculated.

So if I'm right, the Variance has no meaning in reality. It is just used to make a positive number out of all 'the distances of the observations, and the mean'.

So, calculating the Variance is just a step, to get the Standard Deviation. And the Standard Deviation is just an "average" of jobs, which each person is far away from the mean. Are my statements true?

[statisticsfun]

@moguai352 Yes you are correct. The Variance is hard to understand as well because its units are in units squared while the standard deviation is in the same units as the mean. For example if your units in question were meters both the standard deviation and mean would be in meters and variance would be in meters squared. Hence, it is easy to compare the standard deviation and mean because they are both in meters, but hard to grasp the variance because it would be in meters squared.

[latterthought1]

This was better explained than ever before in my years at a very prestigious private school... 

[MeztizaAngie]

Thank you very much

[statisticsfun]

Dear Mom,

5.76 is the square root of 33.2 which is the variance. By definition the standard deviation is the square root of the variance.

I am always trying to improve my channel, so if need other videos just ask.

Good luck in your classes and I hope the video's help you "parent more and study less."

David

[statisticsfun]

Dear Mom,

5.76 is the square root of 33.2 which is the variance. By definition the standard deviation is the square root of the variance.

I am always trying to improve my channel, so if need other videos just ask.

Good luck in your classes and I hope the video's help you "parent more and study less."

David

[MsTravelchic]

I am a Mom returning to school after many years and this has been the BEST YET ON EXPLAINING STANDARD DEVIATION!!! Thank you so much however I was able to follow the entire Video but how did you get the sample standard of 5.76 Jobs?? Good Job you were the best!!!!!