Rugby is often billed as being the geographic center of North America.
As of the census of 2000, there were 2,939 people, 1,291 households, and 765 families residing in the city. The population density was 588.0/km² (1,520.1/mi²). There were 1,434 housing units at an average density of 286.9/km² (741.7/mi²). The racial makeup of the city was 98.09% White, 1.02% Native American, 0.37% Asian, 0.03% from other races, and 0.48% from two or more races. Hispanic or Latino of any race were 0.44% of the population.
The top 6 ancestry groups in the city are German (49.6%), Norwegian (40.5%), Irish (5.3%), English (4.0%), Russian (3.7%), French (3.6%).
There were 1,291 households out of which 26.6% had children under the age of 18 living with them, 49.0% were married couples living together, 8.0% had a female householder with no husband present, and 40.7% were non-families. 37.3% of all households were made up of individuals and 21.2% had someone living alone who was 65 years of age or older. The average household size was 2.17 and the average family size was 2.89.
In the city the population was spread out with 23.1% under the age of 18, 5.4% from 18 to 24, 23.1% from 25 to 44, 20.2% from 45 to 64, and 28.1% who were 65 years of age or older. The median age was 44 years. For every 100 females there were 86.8 males. For every 100 females age 18 and over, there were 81.3 males.
The median income for a household in the city was $25,482, and the median income for a family was $35,745. Males had a median income of $25,885 versus $18,510 for females. The per capita income for the city was $14,380. About 9.6% of families and 13.7% of the population were below the poverty line, including 11.6% of those under age 18 and 19.1% of those age 65 or over.