Why do we divide with n-1 instead of n, when population variance is estimated from the sample? Yes, sample will have less variability, so our estimate based on n will underestimate population variance – so if we divide with something smaller, like n-1, it will be bigger, makes perfect sense. But why n-1?? The argument is that we are getting information from only n-1 independent pieces, because the last one is already given by the mean, therefore only n-1 values are free to vary. I understand the flow of argument and clearly one can determine the last value from average, however I don’t understand how exactly it applies here. If one wanted to determine just sample variance (not as population estimate) than you would divide with n, but you only have n-1 values that are free to vary? So why doesn’t the same logic apply. Also, one can potentially estimate last value from the mean but we are not doing that. Maybe I don’t understand enough statistics yet, but please somebody explain this.