As of the census of 2000, there were 2,757 people, 1,164 households, and 743 families residing in the county. The population density was 4 people per square mile (2/km²). There were 1,418 housing units at an average density of 2 per square mile (1/km²). The racial makeup of the county was 96.37% White, 0.07% Black or African American, 2.36% Native American, 0.15% Asian, 0.07% Pacific Islander, 0.25% from other races, and 0.73% from two or more races. 0.62% of the population were Hispanic or Latino of any race. 44.1% were of Norwegian and 32.5% German ancestry according to Census 2000.
There were 1,164 households out of which 27.70% had children under the age of 18 living with them, 56.40% were married couples living together, 5.00% had a female householder with no husband present, and 36.10% were non-families. 34.20% of all households were made up of individuals and 20.40% had someone living alone who was 65 years of age or older. The average household size was 2.30 and the average family size was 2.96.
In the county the population was spread out with 23.60% under the age of 18, 6.10% from 18 to 24, 22.50% from 25 to 44, 23.10% from 45 to 64, and 24.70% who were 65 years of age or older. The median age was 44 years. For every 100 females there were 95.50 males. For every 100 females age 18 and over, there were 92.30 males.
The median income for a household in the county was $28,642, and the median income for a family was $37,625. Males had a median income of $24,063 versus $20,344 for females. The per capita income for the county was $15,941. About 6.90% of families and 9.70% of the population were below the poverty line, including 11.50% of those under age 18 and 11.00% of those age 65 or over.