I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given:
Some others refer to Bessel's correction. As far as I understood, the variance of the sample underestimates the population variance systematically in magnitude of the variance of the mean. If you subtract this variance and solve the equations, n-1 is left as denominator.
Other authors refer to degrees of freedom: the sample mean is used to estimate the population mean. This value is then fixed in the calculation of the variance and therefore you lose one degree of freedom, resulting in n-1.
I wonder how this two explanations go together. Is it a coincidence that both explanations fit? Is there one right one? Why are even two explanations spread?
English is not my native language, I hope I still got the terms right. Thank you for your answers!