Universal equations for Pythagorean and Sauter-type formulas of mean value calculation and classification of the Extended Pythagorean Means

A general equation, combining the Pythagorean and Sauter-type formulas, which can be used for calculation of a mean of a set of values is given and discussed in the paper. A classification of means, forming the Extended Pythagorean Means family, including power (arithmetic, geometric, quadratic, cubic, etc.), inverted power (harmonic, inverted quadratic, inverted cubic, etc.), and Sauter-type (volumesurface, volume-length, etc.) is presented. The calculated means, depending on their type, are different. Formulas for calculating mean values for a set of values treated individually, in groups and as a fraction (weighted mean) are also given.