According to the United States Census Bureau, the county has a total area of 2,332.7 square miles (6,042 km2), of which 2,326.4 square miles (6,025 km2) is land and 6.3 square miles (16 km2) (0.3%) is water.[4]
As of the 2010 census, there were 7,027 people, 2,466 households, and 1,582 families in the county. The population density was 3.0 inhabitants per square mile (1.2/km2). There were 3,105 housing units at an average density of 1.3 units per square mile (0.50 units/km2). The racial makeup of the county was 92.4% white, 4.4% American Indian, 1.0% black or African American, 0.5% Asian, 0.4% from other races, and 1.3% from two or more races. Those of Hispanic or Latino origin made up 1.7% of the population. In terms of ancestry, 27.9% were German, 19.1% were Irish, 14.6% were English, 8.5% were Norwegian, and 4.7% were American.
Of the 2,466 households, 26.5% had children under the age of 18 living with them, 50.8% were married couples living together, 8.8% had a female householder with no husband present, 35.8% were non-families, and 32.2% of all households were made up of individuals. The average household size was 2.23 and the average family size was 2.79. The median age was 45.1 years.
The median income for a household in the county was $39,851 and the median income for a family was $45,339. Males had a median income of $30,163 versus $24,837 for females. The per capita income for the county was $17,849. About 12.3% of families and 17.3% of the population were below the poverty line, including 32.4% of those under age 18 and 13.0% of those age 65 or over.