On Wed, 02 Aug 2006 22:39:42 -0400, Jerry Dallal <gdallal@SPAM_BLOCK.world.std.com> wrote:
> Bob, > > It would be nice if you did your own homework instead of claiming > immunity because you gave your texts and journals away. You can haul > yourself to a library as easily as any one of us. Since you're retired, > you might be able to do it *more* easily! Instead of complaining that a > mode or median is not an average, you might look at where the notion > came from. With your knowledge of statistics, you're in a better > position than most to sort it out. > > I'm starting to see where "median (and possibly mode) as an average" > came from. Back in 1874, Galton was looking to investigate inheritance > of difference among people, his "statistics by intercomparison". It > involved looking at "deviations from an average". In some instances the > "average" that he felt it was best to consider was the median. It may > well be that the practice predates Galton. I'll let someone else trace > it back farther. > > I'm done with this discussion because I'm tired of doing all the work. > You've now got Galton, Yule, Kendall, Snedecor, Cochran, Wallis, Roberts > all using average as a collective. The concept of "deviations from an > average" seem like an excellent way for this notion to have started. I > don't have the time or interest to pursue it further. > > The historical use of average as a collective, which now has been > demonstrated to span over 100 years(!), is why I tell my students not to > use "average" but instead say whether they are talking about "mean", > "median", or "mode". I don't tell them to ignore 100 years of usage by > some of the leading people in the field. >
Jerry, Thanks for the excellent set of posts.
"Linguistic prescriptivism", which attempts to dictate usages in grammar or words, is usually conservative, trying (too hard?) to preserve the past.
Your information has shown that Bob's attempt to establish "average" as excluding the mode has to be regarded as an unintentional and ignorant break with the past. Well, linguistic drift occurs for all sorts of reasons, and misunderstandings not too different from that one have sometimes won over the common usage.
I think it is interesting that "terrible" and "terrific" originally meant the same thing, which both meant about the same as "awful" and "awesome" did. There is a famous quotation about a new cathedral being terrible and awful, in the words of an admirer.