Alexander attended high school at the M Street High School (later Dunbar High School) in Washington, D.C., where she was encouraged to continue her education by noted historian, Carter G. Woodson. After high school, Alexander was persuaded by her mother to attend the University of Pennsylvania, where the family had strong ties. Her father, Aaron Albert Mossell, was a graduate of Lincoln University and the first African American to graduate from the University of Pennsylvania Law School in 1888. Her uncle, Louis Baxter Moore, was the first African American to receive a Ph.D. from the University of Pennsylvania.

In 1918, Alexander received a B. S. in Education with senior honors, and in 1919, a M.A. in Economics, both from the University of Pennsylvania. In 1921, she received a Ph.D. in economics from the University of Pennsylvania's Wharton School, becoming one of the first black women to receive a doctorate and the first African American to receive a Ph.D. in economics. Her dissertation was entitled, "The Standard of Living among One Hundred Negro Migrant Families in Philadelphia." Alexander was proud of her graduation, "I can well remember marching down Broad Street from Mercantile Hall to the Academy of Music where there were photographers from all over the world taking my picture."

While at the University of Pennsylvania, Alexander was active in the Gamma Chapter of the Delta Sigma Theta Sorority. In 1921, she became the first national president of the national organization of Delta Sigma Theta, serving for five years.

After graduation from the University of Pennsylvania, she became an actuary with the black-owned North Carolina Mutual Life Insurance Company. In 1923, she married Raymond Pace Alexander who had just received his law degree from Harvard University and admitted to the Pennsylvania State Bar. Shortly after her marriage, she returned to college to study for a law degree.

In 1927, she became the first African-American woman to receive a L.L.B. from the University of Pennsylvania Law School. She was also the first African American woman admitted to the State Bar and allowed to practice law in Pennsylvania. After joining her husband's law firm, they fought together against discrimination and segregation in Philadelphia restaurants, hotels, and theaters. She was the first African-American woman to serve as assistant city solicitor of Philadelphia, and was elected secretary of the National Bar Association in 1943, the first woman to hold a national office in the Association.

In 1947, President Harry S. Truman appointed Alexander to the President's Committee on Civil Rights. The report, issued during her tenure, entitled To Secure These Rights, became the basis for future civil rights policy decisions and legislation. In 1959, she opened her own law office and practiced there until 1976 when she joined the law firm of Atkinson, Myers and Archie. While practicing law, Alexander was active in over thirty local and national civic organizations.

In 1974, Alexander received a fifth degree from the University of Pennsylvania, an honorary degree of Doctor of Laws. Part of the citation read: "As an active worker for civil rights, she has been a steady and forceful advocate on the national, state, and municipal scene, reminding people everywhere that freedoms are won not only by idealism but by persistence and will over a long time." In 1978, at the age of eighty-one, Alexander was appointed chairperson of the White House Conference on Aging.

She retired from practice and from public life generally in 1982. Mrs. Alexander died in 1989 and is survived by two daughters, Mary Elizabeth Alexander Brown and Rae Pace Alexander Minter.