I really loved the first argument! Having n-1 at the denominator to have 0/0 when n=1 is such a neat way to mathematically express that from one sample cannot infer anything on the variance!
It is also my favorite argument. I also call it the "interviewee's argument". You can use it in an interview if you are asked to explain this to someone who doesn't know much statistics.
Regarding the compensation argument, doesn't the sample mean minimize the sample variance (understood as a function of the parameter which would take the sample mean's place) regardless of the denominator? If I were to argue the n-1 denominator based solely on this argument I think I could argue for a n-2 denominator and so on...
I really loved the first argument! Having n-1 at the denominator to have 0/0 when n=1 is such a neat way to mathematically express that from one sample cannot infer anything on the variance!
It is also my favorite argument. I also call it the "interviewee's argument". You can use it in an interview if you are asked to explain this to someone who doesn't know much statistics.
Regarding the compensation argument, doesn't the sample mean minimize the sample variance (understood as a function of the parameter which would take the sample mean's place) regardless of the denominator? If I were to argue the n-1 denominator based solely on this argument I think I could argue for a n-2 denominator and so on...
Exactly. It only says a compensation is needed, but doesn't say how much.
So these 4 arguments are ordered in the level of "precise".
My favourite argument is the last one, because it was new to me.
It is also the standard one in a mathematical statistics course.
Which is your favorite argument and which one did you learn in school?