Difference between average case and amortized analysis

Question

I am reading an article on amortized analysis of algorithms. The following is a text snippet.

Amortized analysis is similar to average-case analysis i

Answer 1

1. Consider the computation of the minimum in an unsorted array. Maybe you know that it has O(n) running time but if we want be more precise it does n/2 comparison in the average case. Why this? because we are doing an assumption on data; we are assuming that the minimum can be in every position with the same probability. if we change this assumption, and we say for example that the probability of being in the i position is for example increasing with i, we could prove a different comparison number, even a different asymptotical bound.

2. In the second paragraph the author say that with average case analysis we can be very unlucky and have a measured average case greater than the therotical case; recalling the previous example, if we are unlucky on m different arrays of size n, and the minimum is every time in the last position, than we'll measure a n average case and not a n/2. This can't just happen when a amortized bound is proven.