I disagree with your algebra examples; a student has to get about this far to realize whether or not there is some potential for a math-based career (especially after our generally horrible K-6 arithmetic competence, both computational and straightforward, "cookbook" word problems).
Regarding the mean, median, and mode mantra, my greatest objection is those are all the precollegiate curriculum does over and over again (except for AP Statistics that is mostly used as an excuse for pretending students are anywhere close to AP Calculus in math competence). The mode is truly useless. On small data sets, it is just meaningless. On large data sets, the idea is obvious at a glance and even more informative if the data happens to be bimodal. Regarding mean and median, however, your own "outlier" example (or exaggerated even further) shows why the mean may be more misleading than the median. In a very real sense, the 1 or 2 really do give better information than the 11. Consider our own national economy, for example. A relatively small group of very rich people pay most of the nation's income tax but the average (mean) misleads people into thinking that these very rich people are not paying their "fair share", whatever that might be. The median gives a much more accurate picture of what is underway. Already a much higher percent of the outrageously high salaried income (sometimes over 60% combining federal, state, and local income tax) whereas none of us here hit half that total percent.
At 11:16 AM 1/11/2014, Donald Sauter wrote: >I've just put a web page with my thoughts on math's three-headed >monster, the Mean, Median and Mode. > > http://www.donaldsauter.com/mean-median-mode.htm > >I explain why the last two need chopping off. > >Donald Sauter