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

[@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! :)

[@gmaxmath]

Beautiful explanation. I will share this with my students.

[@datamlistic]

Thanks! Happy to hear that 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. :)

[@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.

[@alnune03]

Thank you! Very good excellent explanation!

[@datamlistic]

Thanks! Happy you enjoyed it! :)

[@bharathishankar4870]

Very Well Explained

[@datamlistic]

Thanks! Glad you liked it! :)

[@szngyun8891]

Thanks for your proofing sir

[@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.

[@piuslau1073]

Hi sir so to sum up using n-1 gives us a better approximation of the population mean when the sample is not the entire population?

[@datamlistic]

Exactly

[@weggquiz]

Well explained

[@datamlistic]

Thank you!

[@Lilk-m7d]

Forte bine ecplicat😢

[@klevisimeri607]

Very nice!

[@datamlistic]

Thanks!

[@rajibkudas123]

5:45 didn't get....whay we can't know X3 if we know X2, X1 & mu

[@datamlistic]

Because mu is the population mean, not the sample mean. Usually, you don't get the exact value of X3 from 3*mu - X2 - X1 as you do if you knew the sample mean of X1, X2, X3 (unless X1, X2, X3 is the entire population...). I hope this makes sense and please let me know if you need further clarification! :)

[@dennisestenson7820]

5:00

[@datamlistic]

?

[@BrunoMorency_perso]

Great video, thanks. Still struggling with the origin of the loss of that degree of freedom at the end. You said "if we have the sample mean, we don't need to know all 3 data points but actually only 2 because the 3rd can be estimated using the sample mean and the other 2 points." This makes sense, I agree that knowing the sample mean and 2 of the 3 points gives you the third. Where I'm struggling is how can you know that sample mean unless all three data points are known and set freely? In other words, how could you know the mean of a sample of three points if you only know two points in that sample? In other words, don't you need to know all three points in order to get the sample mean that you then use to say that third isn't necessary?

[@BrunoMorency_perso]

I think I got through it. So yes, you obviously need to know all values in your sample in order to calculate the sample mean. Where the N-1 comes in is when we then want to calculate the variance of that sample of which you now know the mean. We know from the proof you linked to in your description that sample variance calculated using N is *not* a good estimate of pop. variance since it's biased to too small of a value. Why is it so? Variance of a sample makes no conceptual sense unless the mean of the sample is know and set (variance sets how much elements in the sample differ from the mean). So to figure the sample variance, the mean must be set and once the mean is set, how many elements are free to vary for the sample mean to remain? The answer is N-1 as the Nth is no longer free to vary for the mean to remain as it is. So only N-1 elements actually contribute to the variance of a sample with a given sample mean. Calculating the sample variance with N-1 rather than N will therefore give of a better estimate of the population variance (which would be calculated with N). It's a bit like hiding a ball under 1 of 3 cups. Once you know the ball must be under one of the cups, you only need to check a max of 2 cups to know under which one it will be (because if it's neither cup A nor cup B, it must be cup C, no need to check it).

[@szngyun8891]

Thanks for your proofing sir

[@datamlistic]

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