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Topic: Mean, Median and Mode - the three-headed monster
Replies: 7   Last Post: Jan 25, 2014 11:13 PM

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Bishop, Wayne

Posts: 2,881
Registered: 12/6/04
Re: Mean, Median and Mode - the three-headed monster
Posted: Jan 12, 2014 12:49 AM
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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.

Wayne

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




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