As of the census of 2000, there were 6,259 people, 2,454 households, and 1,700 families residing in the county. The population density was 4/km² (9/mi²). There were 2,733 housing units at an average density of 2/km² (4/mi²). The racial makeup of the county was 99.25% White, 0.05% Black or African American, 0.05% Native American, 0.03% Asian, 0.03% Pacific Islander, 0.30% from other races, and 0.29% from two or more races. 0.89% of the population were Hispanic or Latino of any race.

There were 2,454 households out of which 33.90% had children under the age of 18 living with them, 60.80% were married couples living together, 5.50% had a female householder with no husband present, and 30.70% were non-families. 29.10% of all households were made up of individuals and 16.50% had someone living alone who was 65 years of age or older. The average household size was 2.50 and the average family size was 3.11.

29.10% of the population is under the age of 18, 5.00% from 18 to 24, 24.20% from 25 to 44, 21.40% from 45 to 64, and 20.40% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 99.10 males. For every 100 females age 18 and over, there were 96.40 males.

The median income for a household in the county was $31,444, and the median income for a family was $38,226. Males had a median income of $26,779 versus $18,438 for females. The per capita income for the county was $15,831. About 8.30% of families and 10.40% of the population were below the poverty line, including 11.70% of those under age 18 and 11.60% of those age 65 or over.