## Degrees of freedom in statistics

Degrees of freedom is a term which keeps coming up as I’m trying to understand probability distributions.

Degrees of freedom seem to have to do with calculations involving random numbers where say the mean is known but the numbers which generate the mean aren’t.

You could for example have 4 numbers whose mean is 50. Since their mean is 50 that means that their sum must have been 200.

Now there are obviously a lot of ways to get a sum of 200 using 4 numbers. Maybe it’s –

1 + 1 + 1 + 197

or

10 + 90 + 10 + 90

The important thing to realize is that you can CHOOSE the first 3 numbers as anything but once you’ve chosen 3 numbers that 4th number is out of your control. Its value is going to be whatever it needs to be in order to satisfy the condition of having the sum of those numbers add up to 200.

So in the case above there are 3 degrees of freedom.

I’m honestly not 100% sure why this is important and why all distributions talk about having k degrees of freedom but I’m going to try to find out.