In 2000, there were 1,163 people, 402 households and 303 families living in Plains. The population density was 1,175.8 per square mile (453.6/km²). 82.12% of the people were White, 1.29% were Native American, 14.27% were from other races, and 2.32% were from two or more races. 26.23% of the people were Hispanic or Latino of any race.