Mathematics, Statistics, and the Concept of Average

There are only very few concepts in any subject and if the students understand these then the details in the further literature can be followed easily. The three ways of teaching any subject is intuitive, practical, and mathematical. The history of any subject generally evolves in the above order but at times randomly. But generally the students are taught the other way round! Presently with the internet and enormous computing power the teaching and research in mathematics can be made pleasant with experiments and visualization. A very effective and interesting way of teaching mathematics is to explain the philosophy followed by the historical development with stories. Such an approach would illustrate how almost every concept has gone through a random path to reach the present status. Commencing from a brief discussion of the deductive philosophy of mathematics and probability we consider the inductive statistics and follow how the concept of average characterised by the mean, median, mode and midrange have evolved from antiquity to the present. Lastly to teach or write a book a suggested sequence is the philosophy, historical development of the concepts, details illustrated by computer programs with visualization, term papers and references to classic papers and books.