An Average is a shorthand, abbreviation and/or stereotype used to describe a given population, assortment, or array. The average reduces and eliminates details in favor of a single number or concept e.g. “4.278512.” For instance, a teacher may speak of the average of quiz scores in spelling of her class. An economist may issue a number calling it the mean of incomes of individuals or families in the United States. In an instant the total population is collapsed into a single number furnished to represent everyone (but really no one).
To illustrate part of the extreme non-sense and mischief of averages, we might ask individuals to describe the entire universe in a single word (which is then said to stand for the entire universe). We might say “space” because by reviewing and analyzing the universe much more than 99.999999999% of the universe is space between light and dark matter. The Universe is essentially empty (so different from crowds on earth). Would we thus say that the universe is irrelevant and unimportant because it is nearly all space? Even if the earth were the only inhabited planet with life with a history, science and inventions, would we be willing to dismiss it as irrelevant? Do you see the wisdom of figuring some number to represent the universe (no less silly than any other average)?
With averages we have the mean and median. But what is much more important, vital and interesting is information about the entire population including outliers; clumps of individuals; the variety and frequency distribution of members; densities; bi and tri-model distributions, etc.
What is the average between water and fire? What is the average between a prune and a ballbearing? If these make no sense, how then should be seriously consider other averages where a word or number stands for millions and billions of different and dis-separate things?
“Not a word of his speech was true.” So why would we select one word or number and call it an average as if to speak for the entire population or array? With an average there is no context, no syntax and no placement. How is there separate meaning without context? In a sense averages are (numerical) essays without context. One cannot accurately and fully described a reality by a single word or number. In short, “average” is often a rather useless and misleading concept.