There were 392 households out of which 36.2% had children under the age of 18 living with them, 48.2% were married couples living together, 17.6% had a female householder with no husband present, and 30.6% were non-families. 25.8% of all households were made up of individuals and 13.5% 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 2.99.
In the city the population was spread out with 29.3% under the age of 18, 5.2% from 18 to 24, 26.2% from 25 to 44, 22.4% from 45 to 64, and 16.8% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 84.2 males. For every 100 females age 18 and over, there were 78.1 males.
The median income for a household in the city was $37,262, and the median income for a family was $43,611. Males had a median income of $32,411 versus $23,875 for females. The per capita income for the city was $16,197. About 9.3% of families and 10.4% of the population were below the poverty line, including 14.5% of those under age 18 and 8.5% of those age 65 or over.
Plymouth is the home of the Amador County Fair One feature of the fairgrounds is the historic Amador Sawmill, a steam-powered sawmill typical of those used from the 1850s to the 1940s. The mill operates on a contract basis and during the 4-day fair in July. The Amador Sawmill and Mining Association also maintains a replica of a mine headframe and a collection of historic mining artifacts adjacent to the sawmill.