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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*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...

[pushkargarg]

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.

[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.

[alnune]

Thank you! Very good excellent explanation!

[gmaxmath]

Beautiful explanation. I will share this with my students.

[benlee]

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.

[benlee]

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?