So the average variation is (total variation)/(n-1). This is why we only have 'n-1' things that can vary. Knowing n-1 scores and the sample mean uniquely determines the last score so it is NOT free to vary. It is not free to vary - the sum of the three scores must be 6 or else the sample mean is not 2.

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':

What does high sample variance mean