As of the census of 2010, there were 2,459 people, 1,025 households, and 632 families in the county. The population density was 2.2 inhabitants per square mile (0.85/km2). There were 1,418 housing units at an average density of 1.2 units per square mile (0.46 units/km2). The racial makeup of the county was 98.2% white, 0.2% Asian, 0.1% Pacific islander, 0.2% from other races, and 1.3% from two or more races. Those of Hispanic or Latino origin made up 1.0% of the population. In terms of ancestry, 74.5% were German, 17.7% were Russian, 7.3% were Norwegian, 6.7% were English, and 2.5% were American.
