The Congregational Church of Medway (1874), designed and built by Mansford Cushman, is listed on the National Register of Historic Places
There were 587 households out of which 35.3% had children under the age of 18 living with them, 64.1% were married couples living together, 5.8% had a female householder with no husband present, and 25.4% were non-families. 20.8% of all households were made up of individuals and 7.0% had someone living alone who was 65 years of age or older. The average household size was 2.54 and the average family size was 2.92.
In the town the population was spread out with 24.9% under the age of 18, 6.5% from 18 to 24, 29.1% from 25 to 44, 29.1% from 45 to 64, and 10.4% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 111.2 males. For every 100 females age 18 and over, there were 104.8 males.
The median income for a household in the town was $33,646, and the median income for a family was $40,063. Males had a median income of $42,353 versus $18,917 for females. The per capita income for the town was $15,264. About 8.6% of families and 11.5% of the population were below the poverty line, including 12.4% of those under age 18 and 11.2% of those age 65 or over.