Patagonia is located at 31°32'30" North, 110°45'12" West (31.541743, -110.753428)1.
As of the census2 of 2000, there are 881 people, 404 households, and 239 families residing in the town. The population density is 285.8/km² (738.7/mi²). There are 498 housing units at an average density of 161.6/km² (417.5/mi²). The racial makeup of the town is 86.49% White, 0.00% Black or African American, 0.91% Native American, 0.45% Asian, 0.00% Pacific Islander, 10.56% from other races, and 1.59% from two or more races. 39.50% of the population are Hispanic or Latino of any race.
There are 404 households out of which 22.8% have children under the age of 18 living with them, 47.0% are married couples living together, 8.9% have a female householder with no husband present, and 40.8% are non-families. 35.1% of all households are made up of individuals and 15.3% have someone living alone who is 65 years of age or older. The average household size is 2.18 and the average family size is 2.85.
In the town the population is spread out with 20.9% under the age of 18, 5.3% from 18 to 24, 20.3% from 25 to 44, 32.1% from 45 to 64, and 21.3% who are 65 years of age or older. The median age is 47 years. For every 100 females there are 87.8 males. For every 100 females age 18 and over, there are 85.9 males.
The median income for a household in the town is $25,795, and the median income for a family is $31,000. Males have a median income of $25,625 versus $24,844 for females. The per capita income for the town is $15,325. 25.1% of the population and 18.0% of families are below the poverty line. Out of the total people living in poverty, 36.1% are under the age of 18 and 17.2% are 65 or older.