Variance and Standard Deviation: Why divide by n-1?

This video is so helpful! Thank you!!

Dead set legend. Pretty much replaced my unit's content with your videos. Cant thank you enough.

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This kind educator should be a millionaire! If you read comments on his videos, he's clearly cleaning up after thousands of (unhelpful) Stats and Data Analytics professors around the globe!!!!

truly helpful... tnx

Should the units of the variance be squared, too? ($)x($) = ($)²

what is population mean & how it is different from sample mean?

In last 2 example what will be the values of N and n respectively

thank you, your videos help a lot

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Please help me with my confusion here. If you decrease the denominator, n-1, you increase or "adjust" the numerator. So, does it increase the variance? I don't even know what I'm asking? (so confused &^%(Q^#%#)

I googled why need to divide by n-1, browsed several sites until I landed here.
Thanks for great explanation.

this is more than somewhat informative, ta!

Very Nicely explained! Thanks

Can you explain concept of n-1 in more easier way. What will happens to our estimates if just use n instead of n-1 for calculating variance and SD.

Can you explain with reference of children growth charts which heavily rely on Variance and SD?

Will wait for your reply and a new video explanation! Thanks😀

Thank you for great explanation!

Had to google golden gaytime 😃🍨

Good video. However, my only issue with N-1 is that, I think subtracting 1 from the sample size is not going to cause any significant effect or difference, especially when the sample size is large. N-1 as a denominator will bring about a very small correction to the variance.
This concept of degrees of freedom, to a lay person like me, seems more academic than useful. Please correct me if I'm wrong.

Thank you very much for your video, it was very very good at explaining. But I have one more question, If descriptive statistics do not try to generalize to a population (since there is no uncertainty in descriptive statistics), then why does the sample standard deviation try to best estimate the population mean? Yet it is still considered a descriptive statistic

Brilliant explanation!

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the reason in both cases in mainly historical

there is no real reason not to use the more intuitive average deviation (AKA mean absolute deviation) when differentiability is not a requirement - in fact the logical thing when one is looking for mean deviations would be to do just that, and the argument often given in text books is that stdev also works, which is true of course, but a logically flippant reason

there is also no reason to use n-1 specifically for most purposes when calculating population variance, which is kind of implied by the fact that the -1 makes a tiny difference for any significant amount of samples

Great video! I personally find the idea of "degrees of freedom" to be a confusing and overall nonsense way of describing why we divide by n-1 for sample variance. Inherently, when you are taking a sample n from a population, each observation is independant and could be anything, so there are n degrees of freedom. Its not until you posit that "given the sample mean x_, and these n-1 observations, you can determine what the last ungiven observation is". I think that using the term "degrees of freedom" here makes no sense, and seems to imply that only n-1 of the observations were truly random/independant, which is obviously not the case. Unless the idea od "degrees of freedom" has some other application that I'm not aware of, I think it hould be thrown out entirely, as the way you explained why we divide by n-1 for samples makes far more sense and doesn't imply anything that isn't true.

thanks

Absolutely amazing explanation. May Allah bless you and grant you guidance.

Fabulous explanation sir! Thank you very much!

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Thankyou

Amazing 🤩

thank you for existing

Is there somewhere where it's proven analytically instead of empirically that n-1 is the right adjustment?

Really helpful me sir to conclude sir tq

thank a lot for your clear explaination

I got to this video from one off you other videos, where you mentioned you would go more in detail why divide by n-1. IMO it was alomst the same content and not really more indepth. Im a little disappointed.

Thank you for this..you did a great job at explaining this..

Don't ever stop making videos.

Excellent explanation...crisp, precise and easily understandable. Thank you.

it really helped me sir thank you for this video

I did not understand some things:
1. Why is Σ(x-x')=0? here x' is sample mean? this is during the calculating of degrees of freedom
2. Why is population mean fictional? Why can't we find it in reality? Can't we calculate it sum of observation divided by num of observation?
3. I did not clearly understand why did we need to inflate the estimated value and not decrease it? What if the sample mean was to the left of both the points. Still do we need to inflate the estimated variance?

Excellent presentation

sorry, I thought spending on golden gaytimes is some kind of pub or bar.. ;).. but excellent explanation of these concepts.

I have never seen a better explanation for degrees of freedom , it gave me chills . Thank you

Thanks!

Yay ZedStatistics. These videos are so very valuable to help understand concepts. Great supplemental to classwork! Thanks Justin!

Thank you so much Zed for your teaching materials. For the attachment, is it possible if we have the password to unprotect the sheet? Because I would like to type something on the file to experiment. Thank you!

Very well explained! Thank you