In 1890, 2,150 people lived in Batesville; in 1900, 2,327, in 1910, 3,399; and in 1940, 5,267.
As of the census of 2000, there were 9,445 people, 3,777 households, and 2,383 families residing in the city. The population density was 907.3 people per square mile (350.3/km²). There were 4,146 housing units at an average density of 398.3/sq mi (153.8/km²). The racial makeup of the city was 91.42% White, 4.65% Black or African American, 0.29% Native American, 1.16% Asian, 0.07% Pacific Islander, 1.40% from other races, and 1.01% from two or more races. 2.50% of the population were Hispanic or Latino of any race.
There were 3,777 households out of which 28.5% had children under the age of 18 living with them, 49.4% were married couples living together, 10.5% had a female householder with no husband present, and 36.9% were non-families. 33.8% of all households were made up of individuals and 16.9% had someone living alone who was 65 years of age or older. The average household size was 2.28 and the average family size was 2.92.
In the city the population was spread out with 22.0% under the age of 18, 12.0% from 18 to 24, 25.6% from 25 to 44, 22.2% from 45 to 64, and 18.2% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 88.0 males. For every 100 females age 18 and over, there were 84.1 males.
The median income for a household in the city was $33,133, and the median income for a family was $42,634. Males had a median income of $31,068 versus $20,506 for females. The per capita income for the city was $17,753. About 11.1% of families and 14.5% of the population were below the poverty line, including 15.1% of those under age 18 and 16.6% of those age 65 or over.