Say I'm a classroom teacher and I want to find the average and variance of my class in a recent exam they did. I imagine that I would consider my class the entire population and so when I calculate the variance I would use $n$ as the denominator.
However, what if this same exam is actually set for all students in the state now?
In today's big data world, it could quite possibly be that the state average and variance is calculated over all students in the state, and then again $n$ would be used for the denominator in the variance.
But what if the state average and variance is calculated by taking say, 10 random samples from every school in the state and then the average and variance calculated over all these 10 samples combined? Then I imagine the denominator would be $n-1$ for the variance.
My question is: If Case B is the actually case, to compare my class average and variance to the state average, should I now be calculating my class variance with $n-1$.
My opinion is that I still use $n$ and it is comparable to the estimate of the variance for the state calculated as in case B. However, i do not know for sure and would like some advice.