As of the census of 2000, there were 1,782 people, 725 households, and 508 families residing in the county. The population density was 2 people per square mile (1/km²). There were 962 housing units at an average density of 1 per square mile (0/km²). The racial makeup of the county was 99.33% White, 0.34% Native American, 0.06% Asian, and 0.28% from two or more races. 0.22% of the population were Hispanic or Latino of any race. 63.1% were of German, 17.2% Norwegian and 6.4% Dutch ancestry.
There were 725 households out of which 30.30% had children under the age of 18 living with them, 65.80% were married couples living together, 2.60% had a female householder with no husband present, and 29.90% were non-families. 28.60% of all households were made up of individuals and 15.70% had someone living alone who was 65 years of age or older. The average household size was 2.43 and the average family size was 3.02.
In the county, the population was spread out with 26.40% under the age of 18, 3.50% from 18 to 24, 24.50% from 25 to 44, 23.50% from 45 to 64, and 22.10% who were 65 years of age or older. The median age was 42 years. For every 100 females there were 100.70 males. For every 100 females age 18 and over, there were 98.30 males.
The median income for a household in the county was $28,793, and the median income for a family was $35,938. Males had a median income of $22,128 versus $17,237 for females. The per capita income for the county was $14,117. About 11.20% of families and 14.10% of the population were below the poverty line, including 7.70% of those under age 18 and 22.30% of those age 65 or over.