According to the United States Census Bureau, the town has a total area of, of which, of it is land and is water. Avon is drained by the Sandy River, a tributary of the Kennebec River. Mount Blue, elevation 3,192 feet above sea level, is located in the southwest corner of Avon. The town is crossed by state routes 4 and 149. It borders the towns of Phillips to the north, Strong to the east, Weld to the west, and Temple to the south.
As of the census of 2010, there were 461 people, 216 households, and 126 families residing in the town. The population density was. There were 341 housing units at an average density of. The racial makeup of the town was 98.0% White, 0.7% African American, 0.2% Asian, 0.7% from other races, and 0.4% from two or more races. Hispanic or Latino of any race were 1.1% of the population. There were 216 households, of which 25.5% had children under the age of 18 living with them, 40.3% were married couplesliving together, 12.0% had a female householder with no husband present, 6.0% had a male householder with no wife present, and 41.7% were non-families. 34.3% of all households were made up of individuals, and 17.6% had someone living alone who was 65 years of age or older. The average household size was 2.13 and the average family size was 2.65. The median age in the town was 46.9 years. 21.3% of residents were under the age of 18; 4.9% were between the ages of 18 and 24; 20.9% were from 25 to 44; 35.8% were from 45 to 64; and 17.1% were 65 years of age or older. The gender makeup of the town was 48.2% male and 51.8% female.
2000 census
As of the census of 2000, there were 504 people, 202 households, and 144 families residing in the town. The population density was 12.2 people per square mile. There were 302 housing units at an average density of 7.3 per square mile. The racial makeup of the town was 99.40% White, 0.40% African American, 0.20% from other races. Hispanic or Latino of any race were 0.60% of the population. There were 202 households, out of which 32.7% had children under the age of 18 living with them, 50.5% were married couples living together, 14.4% had a female householder with no husband present, and 28.7% were non-families. 20.3% of all households were made up of individuals, and 8.9% had someone living alone who was 65 years of age or older. The average household size was 2.50 and the average family size was 2.87. In the town, the population was spread out, with 26.4% under the age of 18, 6.2% from 18 to 24, 29.4% from 25 to 44, 25.4% from 45 to 64, and 12.7% who were 65 years of age or older. The median age was 39 years. For every 100 females, there were 93.8 males. For every 100 females age 18 and over, there were 94.2 males. The median income for a household in the town was $29,722, and the median income for a family was $32,250. Males had a median income of $28,125 versus $16,696 for females. The per capita income for the town was $15,573. About 18.4% of families and 20.0% of the population were below the poverty line, including 24.4% of those under age 18 and 25.0% of those age 65 or over.
