In chemical graph theory, many graph parameters, or topological indices, were proposed as estimators of molecular structural properties. Often several variants of an index are considered. The aim is to extend the original concept to larger families of graphs than initially considered, or to make it more precise and discriminant, or yet to make its spread of values similar to that of another index, thus facilitating their comparison. In this paper, we introduce a new variant of the Szeged index. It is named normalized revised Szeged index, and is obtained by taking the square root of the revised Szeged index divided by the number of edges in the considered graph. The spread of its values is the same as for the Randic index. We also study the correlations between the Szeged indices, as well as the Randic index, and the boiling point molecules corresponding to chemical graphs with up to eight vertices.