Questions about calculating free energy error?

[D Y]

Dear all,

  Recently i have learned the class of how to analysis the statistical error in MD (https://www.plumed.org/doc-v2.8/user-doc/html/masterclass-21-2.html), but i was confused about the formular of free energy errors, and  i posted it below. 

In my first glance, the FES error should be calculating as following proceures:

1. Spliting the COLVAR into severals blocks, just like block analysis do.

2. calculating the FES of each block.

3. calculating the variance of FES of these blocks, then we can obtain the error.

so could you please explain the difference between my thought and the above formular to calculate the errors?