It would be nice to make use of the US Census Data for the interpretation of Early Mormonism. But the problems are not without their trickery.
Palmyra belonged to the Phelps and Gorham Purchase and was incorporated in March 29, 1827. While now part of Wayne County, Wayne County itself was only formed April 11th, 1823, when parts of Seneca and Ontario county were combined. Thus, if one wants to study the 1820 census, one has to look at the Ontario county entry, under which Palmyra (unfortunately misspelled as Palnyra in the table) was classified at that time.
Fortunately, the issue does not arise for Sharon, Windsor County, Vermont, where Joseph Smith Jr was born in December 23rd, 1805, as that county had been founded in 1781, and the town was a New Hampshire grant of King George III, and established by settlers from Sharon, Connecticut.