Parma is the birthplace of world-renowned ecologist and soil scientist Dr. Robert E. Horton and NASCAR driver Brian Tyler.
As of the census of 2000, there were 907 people, 310 households, and 233 families residing in the village. The population density was 1,541.2 per square mile (593.6/km²). There were 317 housing units at an average density of 538.7/sq mi (207.4/km²). The racial makeup of the village was 96.14% White, 0.55% African American, 0.88% Native American, 0.55% Asian, 0.66% from other races, and 1.21% from two or more races. Hispanic or Latino of any race were 1.65% of the population.
There were 310 households out of which 43.2% had children under the age of 18 living with them, 58.7% were married couples living together, 11.9% had a female householder with no husband present, and 24.8% were non-families. 21.0% of all households were made up of individuals and 7.1% had someone living alone who was 65 years of age or older. The average household size was 2.86 and the average family size was 3.32.
In the village the population was spread out with 33.7% under the age of 18, 7.2% from 18 to 24, 30.9% from 25 to 44, 19.5% from 45 to 64, and 8.7% who were 65 years of age or older. The median age was 33 years. For every 100 females there were 104.7 males. For every 100 females age 18 and over, there were 98.3 males.
The median income for a household in the village was $39,531, and the median income for a family was $46,429. Males had a median income of $31,307 versus $24,432 for females. The per capita income for the village was $16,483. About 1.8% of families and 3.3% of the population were below the poverty line, including 2.0% of those under age 18 and 9.1% of those age 65 or over.