Why We Divide by N-1 in the Sample Variance (Standard Deviation) Formula | The Bessel's Correction

In this video we discuss why and when we divide by n-1 instead of n in the sample variance and the sample standard deviation formula, known in the statistics literature as the Bessel's correction. This method corrects the bias in the estimation of the population variance. but only partially corrects the bias in the estimation of the population standard deviation (and that's why I didn't include the standard deviation in this video).
References
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Expected value of sample variance proof: proofwiki.org/wiki/Bias_of_Sa...
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Contents
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00:00 - Intro
00:19 - Population vs Sample Statistics
01:22 - Population vs Sample Biased Variance Example
02:13 - Expected Value of the Biased Variance
03:34 - Bias Source Intuition
04:38 - Degrees of Freedom
05:55 - Outro
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#variance #standarddeviation #bias #statistics

[@datamlistic]

I had a small cold while recording the video, hope my voice didn't sound too weird...

[@JoaqoRiquelme]

You were great! Thanks for the effort. I learned a lot.

[@datamlistic]

@@JoaqoRiquelme Thanks a lot! I am happy to hear you found the video helpful! :)

[@pushkargarg4946]

I have been going through other bs videos people be putting using the same number line example, no one even talking about the DOF reason. Great vid man thanks.

[@datamlistic]

Many thanks! Glad you think so about this explanation! :)

[@sayangoon2180]

Crisp and Clear.Thank you

[@datamlistic]

Thanks! Glad you liked it! :)

[@iacobsorina6924]

Very clean explanation! Thank you!😊

[@datamlistic]

Glad it was helpful! :)

[@AlbinJames]

Thanks for this excellent presentation! It's good to see material on such subtle aspects of statistics, and your friendly way of building an intuition around it :) This was way more accessible than the Wikipedia entry and encourages one to continue studying it.

[@datamlistic]

Thank you for your kind words! I am happy to hear that you found this video useful. :)

[@alnune03]

Thank you! Very good excellent explanation!

[@datamlistic]

Thanks! Happy you enjoyed it! :)

[@gmaxmath]

Beautiful explanation. I will share this with my students.

[@datamlistic]

Thanks! Happy to hear that you liked it! :)

[@szngyun8891]

Thanks for your proofing sir

[@bharathishankar4870]

Very Well Explained

[@datamlistic]

Thanks! Glad you liked it! :)

[@klevisimeri607]

Very nice!

[@datamlistic]

Thanks!

[@tutorchristabel]

Well explained

[@datamlistic]

Thank you!

[@user-ot2vx8pd5u]

Forte bine ecplicat😢

[@benlee3545]

Hi DataMlistic, not sure you can share your dataset so that I can know how this population mean=175 is calculated. As I did try a few sample and yes they are all below 175 but how do I know this 175 is derived? Also the USL and LSL if provided will be extremely helpful. Thank you in advance.

[@datamlistic]

Thanks for the question! I simply defined a gaussian with a mean of 175 and a std of 6 and took samples from it, nothing more, nothing less.

[@benlee3545]

@@datamlistic Sir, noted and thank you very much for your reply.

[@benlee3545]

Hi DataMlistic, I try a sample of 160,155,180,190 and I get a Variance of 204 which is far larger than 36. By the way, when we do sampling, we never know the population mean since the population is so big. So how do I know when to use N-1 or bessel correction?

[@datamlistic]

Hi Ben Lee Thanks for the question. How did you calculate the variance, what formula did you use? It seems to be really off? To answer your second question, population is more of a theoretical concept in statistics, and you almost never have access to it. I suggest to alawys use the Bessel correction to compute the variance, unless it's clearly stated that the samples you've got are the entire population.

[@benlee3545]

@@datamlistic Sir, thank you very much.

[@datamlistic]

Glad I could help! :)

[@datamlistic]

Glad I could help! :)

[@benlee3545]

@@datamlistic Yes! That is a big help.

[@dennisestenson7820]

5:00

[@datamlistic]

?

[@szngyun8891]

Thanks for your proofing sir

[@datamlistic]

You're welcome! Glad tou liked it! :)