This paper presents an approach on how the promediation notion is shown in the construction of what is termed the promedial calculus. Show different contexts in which some kind of average is used for carrying out the calculations of areas, finite sums, definite integrals, expected values and other concepts of statistics. Treatment revolves mainly around the arithmetic mean is the prototype of the average, and what is a rescue that epistemology is the excess and defect that stems from considerations of Archimedes.
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