N vs N-1

We discuss when and why you would use N or N-1 in the denominator of a standard deviation or variance formula.
Works Cited:
1) Statistics for Psychology (6th Ed.) by A. Aron, Coups and E. Aron
2) Introduction to the Practice of Statistics (6th Ed.) by Moore, McCabe and Craig

[@manishchoudhary6575]

Great video , I have searched many videos on why n-1 ? , really your video only help . I hope my comment will encourage you .

[@mandy911]

Isnt it the sum total of variance for population is zero and not the case for sample variance we have a negative value left that is why we use -1

[@pmarcum7146]

Sounds like reason for the "-1" boils down to: "we need to make the denominator smaller in order to get a bigger number for variance, in order to account for the sub-sample used for the statistics possibly not representing the full sample." If this reason is the only one, then why not make the denominator even smaller by using "N-2", or even "N-3" and so on? The "-1" is rather arbitrary, if the only reason for using "-1" is the reason that I summarized above. I don't feel as if you have explained why we use the "1" in particular ... what you've explained is that by making the denominator smaller, we get a bigger number for variance. Is there a mathematical proof demonstrating that the inclusion of "-1" for statistics applied to a sub-sample perfectly accounts for the "just using N" variance that would be computed on the full sample? That proof is what I was hoping I would see here!

[@TheStrings-83639]

Yeah there is one I guess. It's called "Bessel's Correction".

[@pranjalikoli9053]

Great... thanks!!

[@anandmaurya2102]

Where are used n and (n-1) for Standard Deviation calculation

[@allround8771]

GREAT!!!

[@antonbj]

you should mention that this only works for large N, in the given example it, of course, makes no sense ;)

[@kowtharhassan882]

Makes no sense at all