As of the census of 2000, there were 1,845 people, 707 households, and 480 families residing in the Monroe. The population density was 521.7 people per square mile (201.2/km2). There were 707 housing units at an average density of 199.9 per square mile (77.1/km2). The racial makeup of the city was 95.83% White, 0.22% African American, 1.41% Native American, 0.27% Asian, 0.11% Pacific Islander, 0.65% from other races, and 1.52% from two or more races. Hispanic or Latino of any race were 5.69% of the population.