Born in Bloomington, Indiana in 1892, the site of Indiana University. He was graduated from Bloomington High School in 1910. He matriculated at Indiana University in the fall of 1910 and was graduated from Indiana University in 1917 with the A.B. degree. He received his M.D. degree from the Medical School of Indiana University in 1919. He practiced medicine in Indianapolis. In 1920, he married Mary Hunter, a teacher in the Indianapolis Public School system. Alexander served several terms as a member of the Grand Board of Directors.