Reef Fish wrote: > Jerry Dallal wrote: >> Reef Fish wrote: >>> Jerry Dallal wrote: >>>> Reef Fish wrote: >>>>> Jerry Dallal wrote: >>>>>> Reef Fish wrote: >>>>>>> Jerry Dallal wrote: > > When there are more than two or three ">"s, its time to either identify > who says what or summarize the issue. In this case, I'll snip > everything > until I get to your single ">" and give my summary response. Anyone > who doesn't understand what we are talking about can go back to > earlier part of the thread. > >> There's a lot to read, especially spread out over many posts, so let me >> summarize: >> >> * There is much confusion over the word "average". >> * My approach, and the one I tell my students, is to avoid the word as a >> stand-alone unmodified noun because there is so much confusion >> surrounding it. They should call a mean a mean, a median a median, a >> mode a mode. > > That much is clear and a repeat of what you had said. > > >> If they have to use the word average, then they'd better >> be sure it's done in a way that is not misunderstood. > > There is more to it than that! Richard Ulrich and Bob O'Hare > understood what an average is, especially if its explained that > it means the ordinary arithmetic average or mean. > > But when THAT is understood by Ulrich and O'Hara, they > continue to muddle over the MODE even though there is no > way in hell you can make the mode of a U-shape distribution > be a mean of that distribution! > > That's where you neglected to consider the LOGIC that if you > want to know hwat a MODE is, you define what it is. And then > it would follow that it CANNOT be any kind of average. no > matter how you define or make your "average" understood. > >> * There is a difference between condoning a practice and trying to >> understand how it came about. >> >> --Jerry > > Well actually it doesn't matter how an ERROR and MISUSE come > about. Your tone was one of condoning the misuse because > many people have misused the definition of a mode, and ergo it's > okay for everyone to misuse it. > >> (How did this thread--not this piece, the entire subject--get started in >> the first place?) > > THIS thread (or sub-thread) was started by Jerry Dallal, to show that > two competent statisticians Wallis and Roberts sinned in 1956, by > carelessly and sloppily written their chapter 7. > > You then used that as an EXCUSE that it okay for others to do the same. > > My point is that the fact that they made the faux pas 50 years ago > does not justify ANYONE's misuse of the term "average" to include > a mode or a median. They did not mistake like some dictionary > writers. But they wrote a sloppy chapter when they should have > labeled the chapter some else such as a term they've used, > "measures of location". > > THEN, there would not have been any question that a mode is > NOT an "average". > > I think we both summarized out positions without having to rehash > the old quotes. > > That was why I changed the subject to: > > MEDIAN and MODE as AVERAGES is NOT to be CONDONED or > TOLERATED, EVER. > > It doesn't matter HOW the error came about, especially if the faux pas > happened 50 years ago. If anyone writes a book with the same > verbiage today, and called the chapter "averages", they should be > raked over the coal by any statistical reviewer who has his salt. > > -- Reef Fish Bob. >
We both see a problem with "average". You hope to reclaim the word. I see it as a lost cause and avoid it instead.
I disagree that Wallis and Roberts were sloppy. Their usage is not an isolated incident. There were other texts around that time with the same type of discussion. My sense from reading the literature is that at that time the profession had decided to use "average" as a catch-all. (BTW, one of my copies of W&R is a 10-th printing from 1965. If it were considered such a bad error, it would likely have been changed.) Who in their right mind would wake up some morning and, by accident, call the mode or mode an average? Perhaps the usage is an example of unintelligent design on the part of some group that wanted to own the terminology by debasing "average" so that the cognoscenti could use "mean', "median", and "mode".
I can remember the first time I was told that "average" is a bad word and should be avoided in favor of "mean", "median", and "mode". My thought was the same as yours. Who would ever think an average was anything *but* an arithmetic mean? However, there were those authorities (W&R, and I believe someone mentioned Huff) saying that "average" could include median or mode, so one had little choice but to go along, that is, avoid using average in favor of mean, median, mode. Perhaps as W&R and similar texts continue to fade from public consciousness it will be possible to reclaim "average".
I do agree completely that "If anyone writes a book with the same verbiage today, and called the chapter "averages", they should be raked over the coal by any statistical reviewer who has his salt."