So Bush Jr. had the lowest approval rating for a president that won a second term. He ended his second term with one of the lowest approval rating of any president of all time (just a short and curly ahead of Nixon).

Some detail:

Including George W. Bush

Approval Shifts:
    Mean Shift: 1.91%
    Standard Deviation: 10.53%
Winning Candidates' Approval Ratings:
    Mean Approval Rating: 50.73%
    Standard Deviation: 11.14%

Excluding George W. Bush

Approval Shifts:
    Mean Shift: 3.60%
    Standard Deviation: 9.40%
Winning Candidates' Approval Ratings:
    Mean Approval Rating: 56.35%
    Standard Deviation: 4.31%

Notice how the standard deviation associated with the winning candidate tightens up significantly with out Bush?

I do publish the results of these analyses, here, on lemmy. However, I just have a day job that has prevented me from doing "the rest" of this analysis. This is only one part of a larger analysis I have planned.

Here are the two distributions: