This paper describes a new mathematical method called conflation for consolidating data from independent experiments that measure the same physical quantity. Conflation is easy to calculate and visualize and minimizes the maximum loss in Shannon information in consolidating several independent distributions into a single distribution. A formal mathematical treatment of conflation has recently been published. For the benefit of experimenters wishing to use this technique, in this paper we derive the principal basic properties of conflation in the special case of normally distributed (Gaussian) data. Examples of applications to measurements of the fundamental physical constants and in high energy physics are presented, and the conflation operation is generalized to weighted conflation for cases in which the underlying experiments are not uniformly reliable.