One of the marathon runners claims that the refreshments stations are two times the number of medical stations. With calculations prove whether this statement is valid or not.

From the map legend, refreshment stations are marked with a blue circle (•).
Counting them on the route: 18 refreshment stations.

From the map legend, medical stations are marked with a red cross inside a circle (⊕).
Counting them on the route: 2 medical stations.

"refreshment stations are two times the number of medical stations".
Number of refreshment stations $= 18$
Number of medical stations $= 2$
According to the claim, Refreshment Stations $= 2 \times$ Medical Stations.

Since $18 \neq 4$, the statement is not valid.

The statement is $\text{not valid}$.