Born in Busti, New York, Plumb attended the common schools. He engaged in mercantile pursuits. He moved to Ohio. He served as member of the State house of representatives in 1855. He studied law. He was admitted to the bar in 1857 and commenced practice in Oberlin, Ohio. During the Civil War served in the Union Army as captain and quartermaster of Volunteers 1861-1865. He was brevetted lieutenant colonel. He moved to Illinois in 1866 and settled in Streator. He engaged in the mining of coal and the building of railroads. He served as mayor of Streator, Illinois from 1882 to 1885.
Plumb was elected as a Republican to the Forty-ninth and Fiftieth Congresses (March 4, 1885-March 3, 1889). He engaged in banking until his death in Streator, Illinois, April 8, 1903. He was interred in Riverview Cemetery.
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