As of the censusGR2 of 2000, there were 1,724 people, 663 households, and 446 families residing in the town. The population density was 298.5/km² (772.4/mi²). There were 735 housing units at an average density of 127.3/km² (329.3/mi²). The racial makeup of the town was 60.90% White, 36.25% African American, 0.41% Native American, 0.75% Asian, 0.58% from other races, and 1.10% from two or more races. Hispanic or Latino of any race were 1.39% of the population.
There were 663 households out of which 31.2% had children under the age of 18 living with them, 42.1% were married couples living together, 21.9% had a female householder with no husband present, and 32.7% were non-families. 28.1% of all households were made up of individuals and 15.2% had someone living alone who was 65 years of age or older. The average household size was 2.60 and the average family size was 3.21.
In the town the population was spread out with 28.7% under the age of 18, 9.3% from 18 to 24, 25.5% from 25 to 44, 19.7% from 45 to 64, and 16.9% who were 65 years of age or older. The median age was 35 years. For every 100 females there were 85.4 males. For every 100 females age 18 and over, there were 78.0 males.
The median income for a household in the town was $22,446, and the median income for a family was $30,685. Males had a median income of $28,125 versus $17,105 for females. The per capita income for the town was $10,495. About 20.8% of families and 29.3% of the population were below the poverty line, including 42.3% of those under age 18 and 24.0% of those age 65 or over.
Independence has a large Italian American community, and boasts an Italian festival every year in April.
