Estimate the partition function by analyzing a graphic

[LCSphysicist]

Homework Statement

All below.

Relevant Equations

All below

I am not sure, but since the partition function Z is just the sum of all Boltzmann Factor

We can just add:

(some terms don't appear in the image, by the way, the estimative is nice, the result is above ANS)

But i didn't understand what the author did:

While i didn't even care about the image of the functions (P(s), what he call by height), his resolution is based on it, not only, he talk nothing about the estimative of the exponents (the values on the abscissa), while my resolution is based on it.

What method he used?? Do you understand?

 

[haruspex]

I was confused at first because the first two terms of your sum are missing. What I see starts at $+e^{-0.7}$.
The author is doing the same as you, but instead of measuring the x coordinates off the graph and computing each y coordinate, he is measuring the y values directly. This gives him cm rather than the actual Boltzmann factor, but he is only interested in ratios of values since it is going to be normalized to a total of 1 anyway.