As of the census of 2000, there were 21,127 people, 8,203 households, and 6,012 families residing in the county. The population density was 40 people per square mile (15/km²). There were 8,909 housing units at an average density of 17 per square mile (6/km²). The racial makeup of the county was 98.53% White, 0.09% Black or African American, 0.25% Native American, 0.12% Asian, 0.10% from other races, and 0.91% from two or more races. 0.57% of the population were Hispanic or Latino of any race.
There were 8,203 households out of which 35.70% had children under the age of 18 living with them, 57.20% were married couples living together, 11.80% had a female householder with no husband present, and 26.70% were non-families. 24.30% of all households were made up of individuals and 9.50% had someone living alone who was 65 years of age or older. The average household size was 2.55 and the average family size was 3.02.
In the county, the population was spread out with 26.10% under the age of 18, 10.30% from 18 to 24, 28.70% from 25 to 44, 23.60% from 45 to 64, and 11.30% who were 65 years of age or older. The median age was 35 years. For every 100 females there were 97.40 males. For every 100 females age 18 and over, there were 94.00 males.
The median income for a household in the county was $24,093, and the median income for a family was $28,595. Males had a median income of $24,721 versus $19,451 for females. The per capita income for the county was $12,927. About 17.60% of families and 20.20% of the population were below the poverty line, including 24.10% of those under age 18 and 17.10% of those age 65 or over.
Scott County, a part of the Cumberland Plateau, includes the majority of the Big South Fork National Park.