At the 2000 census, there were 10,155 people, 4,101 households and 2,837 families residing in the county. The population density was 6 per square mile (2/km²). There were 4,791 housing units at an average density of 3 per square mile (1/km²). The racial makeup of the county was 97.22% White, 0.10% Black or African American, 0.29% Native American, 0.17% Asian, 1.62% from other races, and 0.60% from two or more races. 2.93% of the population were Hispanic or Latino of any race. 43.2% were of Norwegian, 12.1% Polish, 11.7% German and 9.6% Swedish ancestry according to Census 2000.
There were 4,101 households of which 30.20% had children under the age of 18 living with them, 60.20% were married couples living together, 5.40% had a female householder with no husband present, and 30.80% were non-families. 28.70% of all households were made up of individuals and 15.10% had someone living alone who was 65 years of age or older. The average household size was 2.45 and the average family size was 3.01.
Age distribution was 25.40% under the age of 18, 6.70% from 18 to 24, 24.70% from 25 to 44, 24.70% from 45 to 64, and 18.50% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 103.20 males. For every 100 females age 18 and over, there were 102.10 males.
The median household income was $34,804, and the median family income was $41,908. Males had a median income of $30,051 versus $20,600 for females. The per capita income for the county was $16,317. About 6.90% of families and 9.80% of the population were below the poverty line, including 11.30% of those under age 18 and 12.80% of those age 65 or over.