As of the census of 2000, there were 4,385 people, 1,752 households, and 1,270 families residing in the county. The population density was 4 people per square mile (1/km2). There were 2,002 housing units at an average density of 2 per square mile (1/km2). The racial makeup of the county was 97.04% White, 0.27% Black or African American, 1.16% Native American, 0.11% Asian, 0.07% Pacific Islander, 0.34% from other races, and 1.00% from two or more races. 1.32% of the population were Hispanic or Latino of any race. 25.5% were of German, 14.5% English, 12.9% Irish, 9.9% Norwegian and 6.3% French ancestry according to Census 2000. 98.0% spoke English and 1.3% German as their first language.

There were 1,752 households out of which 30.10% had children under the age of 18 living with them, 61.40% were married couples living together, 6.90% had a female householder with no husband present, and 27.50% were non-families. 24.10% of all households were made up of individuals and 9.90% had someone living alone who was 65 years of age or older. The average household size was 2.47 and the average family size was 2.91.

In the county the population was spread out with 25.20% under the age of 18, 4.80% from 18 to 24, 26.20% from 25 to 44, 27.40% from 45 to 64, and 16.40% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 104.00 males. For every 100 females age 18 and over, there were 103.70 males.

The median income for a household in the county was $32,689, and the median income for a family was $36,524. Males had a median income of $28,495 versus $19,500 for females. The per capita income for the county was $16,237. About 7.60% of families and 10.80% of the population were below the poverty line, including 13.70% of those under age 18 and 7.90% of those age 65 or over.

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