As of the census of 2000, there were 7,453 people, 3,127 households, and 1,976 families residing in the county. The population density was 4 people per square mile (2/km²). There were 3,812 housing units at an average density of 2 per square mile (1/km²). The racial makeup of the county was 90.51% White, 0.32% Black or African American, 6.05% Native American, 0.23% Asian, 0.05% Pacific Islander, 0.30% from other races, and 2.54% from two or more races. 1.74% of the population were Hispanic or Latino of any race. 33.6% were of German, 12.1% English, 9.5% Norwegian and 7.0% Irish ancestry according to Census 2000.
There were 3,127 households out of which 23.70% had children under the age of 18 living with them, 50.90% were married couples living together, 8.50% had a female householder with no husband present, and 36.80% were non-families. 32.70% of all households were made up of individuals and 14.60% had someone living alone who was 65 years of age or older. The average household size was 2.23 and the average family size was 2.82.
In the county, the population was spread out with 22.80% under the age of 18, 5.80% from 18 to 24, 20.60% from 25 to 44, 28.30% from 45 to 64, and 22.50% who were 65 years of age or older. The median age was 46 years. For every 100 females there were 109.80 males. For every 100 females age 18 and over, there were 103.80 males.
The median income for a household in the county was $29,631, and the median income for a family was $37,827. Males had a median income of $30,646 versus $20,017 for females. The per capita income for the county was $17,048. About 7.80% of families and 13.60% of the population were below the poverty line, including 18.90% of those under age 18 and 9.80% of those age 65 or over.