Média aritmética ponderada : um estudo detalhado da influência dos pesos no posicionamento da média. Propriedades e aplicações

Abstract

The concept of Arithmetic Mean is quite simple and used in various situations of everyday life. However, the concept that is fundamentally taught is Arithmetic Mean as an equal division, with little reflective usage of the algorithms that calculate such average. The present study extends the concept of Arithmetic Mean for the idea of equilibrium point, studying the potential of the topic and its various applications in mathematics and in other areas of knowledge. Expanding this concept, a proposal for calculating means from its geometric interpretation is presented. Such an interpretation becomes possible after detailed study of the influence of weights in mean position and resulting properties from the expansion of the concept. Learning the essence makes possible the discovery of shortcuts to the resolution of issues associated with the topic. It is emphasized that mental arithmetic and proportional thinking are important means for the exercise of citizenship, since physical or electronic elements to perform such procedures may be unavailable. Moreover, in the end of high school, students who wants to be admitted in university must be submited to Novo Enem proof, in which resolution time of the issues becomes part of the evaluation, given the high number of questions. The paper presents a multipronged and effective approache, able to contribute to students and teachers formation through a significant learning approach.