I've just read something about calculating sample standard deviation. Some explanations say that it is because of degree of freedom. With a constraint that the mean should be zero, we do actually have only n-1 degree of freedom. Well, this explanation is pretty convincing.
But there is still another question stick in my mind. If the degree of freedom of sample data is n-1 due to the constraint, then the same constraint also apply to the full data set. So it seems to me that when calculating standard deviation of full data set, we should also use n-1 as denominator. Can any one explain this to me why we don't use n-1 for the full data set?
Please give warm help to a math beginners :)