As of the census of 2000, there were 6,634 people, 2,689 households, and 1,801 families residing in the county. The population density was 4/km² (12/mi²). There were 2,990 housing units at an average density of 2/km² (5/mi²). The racial makeup of the county was 97.75% White, 0.21% Black or African American, 0.44% Native American, 0.06% Asian, 0.02% Pacific Islander, 0.83% from other races, and 0.69% from two or more races. 1.66% of the population were Hispanic or Latino of any race.
There were 2,689 households out of which 30.20% had children under the age of 18 living with them, 59.10% were married couples living together, 5.00% had a female householder with no husband present, and 33.00% were non-families. 30.20% of all households were made up of individuals and 16.30% had someone living alone who was 65 years of age or older. The average household size was 2.37 and the average family size was 2.95.
In the county the population was spread out with 26.30% under the age of 18, 5.10% from 18 to 24, 24.00% from 25 to 44, 23.30% from 45 to 64, and 21.30% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 93.50 males. For every 100 females age 18 and over, there were 91.30 males.
The median income for a household in the county was $35,162, and the median income for a family was $41,725. Males had a median income of $29,813 versus $18,507 for females. The per capita income for the county was $17,465. About 4.80% of families and 7.80% of the population were below the poverty line, including 8.20% of those under age 18 and 10.00% of those age 65 or over.