He graduated from Michigan State University in 1914, with a bachelor's degree in mechanical engineering.

Prior to joining the Eisenhower administration, Mueller served in multiple posts at the Department of Commerce.

In 1956, Mueller was charged with the heading of the Division of Domestic Affairs, and in 1958, he was elevated to deputy secretary, the number two position in the bureau.

He married the former Mary Darrah on November 6, 1915; they had two children, Marcia Joan and Frederick Eugene Mueller.

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