According to theUnited States Census Bureau, the county has a total area of 4,350 square miles (11,300 km2), of which 4,340 square miles (11,200 km2) is land and 11 square miles (28 km2) (0.2%) is water.[5]
As of the2010 census, there were 11,586 people, 5,099 households, and 3,202 families living in the county. The population density was 2.7 inhabitants per square mile (1.0/km2). There were 5,836 housing units at an average density of 1.3 per square mile (0.50/km2). The racial makeup of the county was 96.6% white, 1.2% American Indian, 0.2% black or African American, 0.2% Asian, 0.2% from other races, and 1.5% from two or more races. Those of Hispanic or Latino origin made up 1.5% of the population. In terms of ancestry, 30.8% wereGerman, 15.9% wereEnglish, 14.7% wereNorwegian, 12.8% wereIrish, and 4.2% wereAmerican.
Of the 5,099 households, 23.8% had children under the age of 18 living with them, 52.9% were married couples living together, 6.5% had a female householder with no husband present, 37.2% were non-families, and 32.6% of all households were made up of individuals. The average household size was 2.18 and the average family size was 2.75. The median age was 47.8 years.
The median income for a household in the county was $37,607 and the median income for a family was $48,623. Males had a median income of $35,110 versus $21,225 for females. The per capita income for the county was $22,295. About 12.5% of families and 14.7% of the population were below thepoverty line, including 24.2% of those under age 18 and 9.3% of those age 65 or over.