Descriptive statistics offer us several averages for a given set of variable numbers. Most elementary courses introduce the mean (i.e., arithmetic mean), the median and the mode.<br>On average, which is supposed to characterize a given distribution of values, is never identical with all the values (except for the trivial case). Each possible suggestion of an average involves some inaccuracy. The answer to the question "what is the best representation of the numbers?" depends on what is meant by "best representation". One could interpret this to mean that the average incurs the least possible "cost" in terms of differences between the average and the actual values. Each definition of the "cost" could be minimized by an appropriate average. Asking students to pay (symbolically) the costs of the errors incurred through use of different averages might introduce the averages via the idea of the least combined error.<br><br>The following procedure, which may be represented as a game in the classroom, has helped my students on both secondary school and college level.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education