As of the census of 2000, there were 3,242 people, 1,358 households, and 890 families residing in the county. The population density was 3 people per square mile (1/km²). There were 1,596 housing units at an average density of 1 per square mile (1/km²). The racial makeup of the county was 98.98% White, 0.03% Black or African American, 0.15% Native American, 0.03% Asian, 0.15% from other races, and 0.65% from two or more races. 0.68% of the population were Hispanic or Latino of any race. 41.1% were of German, 28.1% Norwegian, 5.3% Irish and 5.0% Polish ancestry according to Census 2000.
There were 1,358 households out of which 29.50% had children under the age of 18 living with them, 59.50% were married couples living together, 4.10% had a female householder with no husband present, and 34.40% were non-families. 31.50% of all households were made up of individuals and 17.20% had someone living alone who was 65 years of age or older. The average household size was 2.32 and the average family size was 2.95.
In the county the population was spread out with 24.10% under the age of 18, 5.30% from 18 to 24, 24.60% from 25 to 44, 24.20% from 45 to 64, and 21.80% who were 65 years of age or older. The median age was 43 years. For every 100 females there were 94.60 males. For every 100 females age 18 and over, there were 96.60 males.
The median income for a household in the county was $31,906, and the median income for a family was $39,485. Males had a median income of $28,682 versus $17,992 for females. The per capita income for the county was $17,662. About 5.90% of families and 8.20% of the population were below the poverty line, including 9.90% of those under age 18 and 10.40% of those age 65 or over.