Wright was born in July 1840, in Dunbarton, New Hampshire. He was studying law when he deferred his education to enlist as a private in the Union army in 1862. He was quickly promoted, becoming a colonel in 1864 before ending the war as an adjunct general under General Sheridan. After the war, he was admitted to the bar of New Hampshire, Massachusetts, and the United States.

In 1872, he won a seat in the Massachusetts Senate, where he served until becoming chief of the Massachusetts Bureau of Labor and Statistics from 1873 until 1878.

Wright became commissioner of labor in 1885, which is the office from which he also led the census at the end of the 1890 publication period. In 1894, he served as chairman of the commission organized to investigate the Pullman Company strike in Chicago, Illinois. Eight years later, he sat on a similar commission, investigating a coal miners’ strike that had occurred earlier that year.

Wright took over leadership a the Census Office after the departure of Robert Porter, finishing the publication of reports from the census of 1890. He was a strong proponent of a permanent census office.

During his time in Washington, Wright was a professor at several universities, including Catholic University and Harvard. In 1902, he left Washington to take a position as the president of Clark College in Massachusetts, also acting as a professor of statistics and socioeconomics from 1904 until his death in 1909.