The Town of Friendship is near the center of Allegany County and is northeast of Olean, New York.
As of the census of 2000, there were 1,927 people, 770 households, and 514 families residing in the town. The population density was 53.2 people per square mile (20.5/km²). There were 994 housing units at an average density of 27.4/sq mi (10.6/km²). The racial makeup of the town was 96.57% White, 1.87% Black or African American, 0.10% Native American, 0.16% Asian, 0.57% from other races, and 0.73% from two or more races. Hispanic or Latino of any race were 0.57% of the population.
There were 770 households out of which 28.6% had children under the age of 18 living with them, 51.7% were married couples living together, 10.5% had a female householder with no husband present, and 33.2% were non-families. 27.4% of all households were made up of individuals and 12.5% 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 3.04.
In the town the population was spread out with 26.2% under the age of 18, 8.7% from 18 to 24, 26.8% from 25 to 44, 23.0% from 45 to 64, and 15.3% who were 65 years of age or older. The median age was 36 years. For every 100 females there were 99.1 males. For every 100 females age 18 and over, there were 94.5 males.
The median income for a household in the town was $26,439, and the median income for a family was $33,542. Males had a median income of $26,440 versus $22,132 for females. The per capita income for the town was $12,552. About 17.1% of families and 21.5% of the population were below the poverty line, including 28.0% of those under age 18 and 7.5% of those age 65 or over.