According to the United States Census Bureau, the town has a total area of 15.7 square miles (41 km²), of which, 15.5 square miles (40 km²) of it is land and 0.2 square miles (0.52 km²) of it (1.53%) is water. Most of the water of that is Andover Lake.

As of the 2010 United States Census Andover had a population of 3,303. The racial composition of the population was 95.9% white, 1.1% black or African American, 0.1% Native American, 1.1% Asian, 0.5% from some other race and 1.2% reporting two or more race. 1.6% of the population was Hispanic or Latino of any race.

As of the census of 2000, there were 3,036 people, 1,150 households, and 861 families residing in the town. The population density was 196.4 people per square mile (75.8/km²). There were 1,198 housing units at an average density of 77.5 per square mile (29.9/km²). The racial makeup of the town was 96.64% White, 0.92% African American, 0.33% Native American, 0.46% Asian, 0.69% from other races, and 0.96% from two or more races. Hispanic or Latino of any race were 1.55% of the population.

There were 1,150 households out of which 37.5% had children under the age of 18 living with them, 64.3% were married couples living together, 8.0% had a female householder with no husband present, and 25.1% were non-families. 19.0% of all households were made up of individuals and 5.6% had someone living alone who was 65 years of age or older. The average household size was 2.64 and the average family size was 3.04.

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