Think of it this way. An average is just a way of finding the midpoint within a bunch of numbers.
What’s the average of 1,2,3,4? It’s 2.5. It’s right in the middle.
What’s the average of 1 and 2? 1.5.
What’s the average of 3 and 4? 3.5.
I don’t know how to explain why they aren’t the same. But if you really understand what an average is, you should be able to understand why your logic isn’t logical.
When comparing salaries, I always thought a “median” was much more useful.
And misapplying the distributive and/or associative property can cause confusion.
That’s as may be, but suppose we concentrate on the OP’s understanding of “average”, which in this context means “mean”. Samantha Leigh, do you understand that if you want the average of four numbers, you have to add them and divide them by four - and that adding them two at a time and dividing each group of two by two, then adding the results, is pretty much guaranteed to not do that for you?