Why was the first compiler written before the first interpreter?

(credit: Stack Exchange)

This Q&A is part of a weekly series of posts highlighting common questions encountered by technophiles and answered by users at Stack Exchange, a free, community-powered network of 100+ Q&A sites.

anguyen asks:

The first compiler was written by Grace Hopper in 1952 while the Lisp interpreter was written in 1958 by John McCarthy's student Steve Russell. Writing a compiler seems like a much harder problem than an interpreter. If that is so, why was the first compiler written six years before the first interpreter?