Winchester is a city in White River Township, Randolph County, in the U.S. state of Indiana. The population was 4,935 at the 2010 census. The city is the county seat of Randolph County. It is the home of Winchester Speedway. History Winchester was laid out in 1818 as the county seat. A post office has been in operation at Winchester since 1820. The Gen. Asahel Stone Mansion, Winchester Courthouse Square Historic District, and Winchester Residential Historic District are listed on the National Register of Historic Places. Geography Winchester is located at (40.173165, -84.977435). According to the 2010 census, Winchester has a total area of , of which (or 99.61%) is land and (or 0.39%) is water. Demographics 2010 census At the 2010 census there were 4,935 people, 2,051 households, and 1,281 families living in the city. The population density was . There were 2,349 housing units at an average density of . The racial makeup of the city was 96.1% White, 0.5% African American, 0.5% Native American, 0.5% Asian, 1.3% from other races, and 1.1% from two or more races. Hispanic or Latino of any race were 2.6%. Of the 2,051 households 30.2% had children under the age of 18 living with them, 43.1% were married couples living together, 14.3% had a female householder with no husband present, 5.0% had a male householder with no wife present, and 37.5% were non-families. 32.2% of households were one person and 14.9% were one person aged 65 or older. The average household size was 2.32 and the average family size was 2.89. The median age was 40.2 years. 23.6% of residents were under the age of 18; 8.3% were between the ages of 18 and 24; 23.8% were from 25 to 44; 25.4% were from 45 to 64; and 18.9% were 65 or older. The gender makeup of the city was 47.6% male and 52.4% female. 2000 census At the 2000 census there were 5,037 people, 2,171 households, and 1,350 families living in the city. The population density was . There were 2,377 housing units at an average density of . The racial makeup of the city was 98.31% White, 0.24% African American, 0.26% Native American, 0.30% Asian, 0.32% from other races, and 0.58% from two or more races. Hispanic or Latino of any race were 1.41%. Of the 2,171 households 27.4% had children under the age of 18 living with them, 48.1%