I'll put up a non-traditional answer: Feynman Diagrams (i.e. not statistical, but definately data related).
Feynman Diagrams are a tool for organizing computations in field theories in physics.
Feynman first invented them to organize terms in computations in quantum electrodynamics (QED) (so the "data" being organized here are the terms in a very difficult computation). They are a combinatorial device used to encode all the ways in which certain events can occur in QED, or more formally, all the terms appearing in a mathematical expansion for the probability amplitude of an event.
They way they organized the data occurring in these computations allowed Feynman to show that QED did not produce infinite probabilities, an achievement called renormalization, for which he won a Nobel prize. Two other men, Julian Schwinger and Sin-Itiro Tomonaga, also won a Nobel for the same achievement, but it is Feynman's techniques, aided by his diagrams, that have stood the test of time.
A famous example is the Penguin Diagram
which were invented when physicists were discovering that some very natural symmetries did not hold in nature (parity and charge conjugation).