In the Nebraska license plate system, Nance County is represented by the prefix 58 (it had the fifty-eighth-largest number of vehicles registered in the county when the license plate system was established in 1922).
1870 - 44 1880 - 1,212 1890 - 5,773 1900 - 8,222 1910 - 8,926 1920 - 8,712 1930 - 8,718 1940 - 7,653 1950 - 6,512 1960 - 5,635 1970 - 5,142 1980 - 4,740 1990 - 4,275 2000 - 4,038
As of the census of 2000, there were 4,038 people, 1,577 households, and 1,107 families residing in the county. The population density was 9 people per square mile (4/km²). There were 1,787 housing units at an average density of 4 per square mile (2/km²). The racial makeup of the county was 98.39% White, 0.37% Native American, 0.05% Asian, 0.45% from other races, and 0.74% from two or more races. 1.14% of the population were Hispanic or Latino of any race.
There were 1,577 households out of which 32.80% had children under the age of 18 living with them, 60.50% were married couples living together, 5.60% had a female householder with no husband present, and 29.80% were non-families. 27.60% of all households were made up of individuals and 13.80% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 3.05.
In the county the population was spread out with 27.90% under the age of 18, 6.80% from 18 to 24, 23.60% from 25 to 44, 22.00% from 45 to 64, and 19.70% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 104.20 males. For every 100 females age 18 and over, there were 101.90 males.
The median income for a household in the county was $31,267, and the median income for a family was $38,717. Males had a median income of $25,349 versus $19,044 for females. The per capita income for the county was $16,886. About 10.20% of families and 13.10% of the population were below the poverty line, including 17.20% of those under age 18 and 9.30% of those age 65 or over.