Analytical intelligence involves logical thinking, and is mostly associated with academic tasks. Solving a math problem or semantic analogies require the use of this component.
As it deals with abstract reasoning, analytical intelligence also implies comparing and evaluating different factors in order to solve a problem efficiently.
The Secretary of State does many things, but is mostly a representative for the United Sates, and goes to other countries and represents the US, trying to get allies or show what we are like.