What can they second data point be? It absolutely MUST be 2. The second data point could be anything, let's say it is 3. The first data point could be anything, let's say it is 1. You calculate the sample mean and it comes out to be 2. There are N things that can vary about the population mean but only N-1 that can vary about the sample mean.
Why!? I mean surely there are N things that can vary about xbar i.e.
The denominator is the amount of things that are able to vary. The numerator is a measure of the total amount of variation Look at the numerator and the denominator in the sample variance equation. If this is truly what the equation is measuring then it should be (total amount of variation)/(number of things that can vary). Think of the whole equation as the average amount of variation. I'll have a go at explaining the intuition between the '1' in 'n-1':
