There is a very strong relationship with population, except that the most extreme disapproval can occur in a state of any size.
Columns are by approval quintile, with highest approval on the left, rows are by population, with greatest population at top.
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Among the 10 highest approval ratings, Jody Rell is from the most populous state (Connecticut is 29th), and probably benefits from her recent promotion. 6 of the 10 most approved governors are from the 10 smallest states. For these smallest states, Carcieri (R-RI) and Lingle (R-HI) are slight underperformers, perhaps reflecting being Republicans in strongly Democratic states.
The most approved big state governor is Sonny Perdue (R-GA). His 19th rating is barely into the 2nd quintile, and Georgia is only the 10th most populated.
Murkowski (R-AK) 46 in approval and 48th in population, Minter (D-DE) 44 and 45, Baldacci (D-ME) 43 and 40, Fletcher (R-KY) 48 and 25, Blanco (D-LA) 45 and 22, and Blunt (R-MO) 47 and 17, demonstrate that it is possible to be highly disapproved in a somewhat smaller state, though it is nearly impossible to have a high approval rating in a larger state.
Of the governors from the 25 most populous states, only 6, Bush (R-FL), Perdue (R-GA), Easley (D-NC), Warner (D-VA), Napolitano (D-AZ), and Owens (R-CO) are among the 25 most approved. All are among the fast growing states.