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Posted: 08 August 2007 06:07 AM   [ Ignore ]
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I heard “On average between 50 and 60 volcanoes erupt every year” in a documentary just now.
Shouldn’t averages be a specific number, in this case 55?
Or else lose “on average” from the above sentence?

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Posted: 08 August 2007 06:33 AM   [ Ignore ]   [ # 1 ]
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It depends on what your purpose is. If you’re doing math, then an average is a specific number, but “average” isn’t always used in a perfectly mathematical sense. “The average Joe” isn’t a mathematical idea, it’s more of a feeling. If you want to convey a feeling instead of mathematical precision, then you use a statement such as the one in the documentary. Even documentaries have to be entertaining and feelings always connect better than concepts.

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Posted: 08 August 2007 08:17 AM   [ Ignore ]   [ # 2 ]
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venomousbede - 08 August 2007 06:07 AM

I heard “On average between 50 and 60 volcanoes erupt every year” in a documentary just now.
Shouldn’t averages be a specific number, in this case 55?
Or else lose “on average” from the above sentence?

The statement also conveys that there are usually at least 50 and fewer than 61. 
Also, you cannot derive that the average is 55, only that it is between 50 and 60.

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Posted: 08 August 2007 08:24 AM   [ Ignore ]   [ # 3 ]
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So wouldn’t “Between 50 and 60 volcanoes erupt every year” be better? The “on average” struck me as redundant.

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Posted: 08 August 2007 09:20 AM   [ Ignore ]   [ # 4 ]
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Average is not a precise mathematical term. The specific number you are referring to is the arithmetic mean. You can also have the median value (where 50% of the values in the set are greater than and 50% less than) or the mode (the most commonly occurring value in the set) or any one of a variety of other methods of calculating an “average.”

(For example given the set (0, 0, 1, 2, 3, 4, 5, 6, 6, 6, 7, 7, 11), the arithmetic mean is 4.46; the median is 5; and the mode is 6. All of these are “averages.")

Average, in the general sense, simply means the expected value that one one should obtain. It is often used more specifically to be synonymous with the arithmetic mean, but this is not the only or “correct” sense. So the narrator of the documentary is using the word quite properly.

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Posted: 08 August 2007 05:58 PM   [ Ignore ]   [ # 5 ]
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venomousbede - 08 August 2007 08:24 AM

So wouldn’t “Between 50 and 60 volcanoes erupt every year” be better?

No, because in any given year the total might be 42, or 69.

One reason to give a range rather than a precise value of an average is because the precise value often doesn’t make sense: consider an average value of 2.4 children per family. Then it is better to say “the average family has 2 to 3 children”.

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Posted: 09 August 2007 04:11 AM   [ Ignore ]   [ # 6 ]
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"Average”, as Dave points out, is not a precise mathematical term. it is one of those Humpty-Dumpty type words which can be made to mean anything the user wants. Its imprecision, together with the fact that it does have vague technical associations for a lot of people (look at the dialogue between Myridon and the OP in this thread), makes it a word beloved of people occupied in marketing. Marketing people are always looking for ways to make non-truth sound true, and to imply meaning where no meaning exists ("five out of six doctors recommend Gunko") --- and words like “average” are a godsend to them. Scientists and technical people, to whom precision is important, eschew the use of “average” and other words like it.

Dave’s explanation is succint and easy to understand. In my opinion he’s too kind to the word, or rather to those who use it. I’m with venomousbede: it shouldn’t be used in a documentary sufficiently technical to deal with the frequency of volcanic events; there, it’s a positive encouragement to fuzzy thinking.

The WIKIPEDIA article gives rigorous definitions of a whole variety of “averages”.  it also tells a little about the etymology of the word (of which i’d previously no idea --- marine insurance of all things!). The book that first made statistics and probability theory understandable to me was “Facts From Figures” by M.J. Moroney (Pelican Books) --- a lucid, witty, immensely readable little masterpiece. Moroney gives a number of amusing examples of the ways in which marketers, politicians, spin doctors --- anybody with an axe to grind --- can (and do) abuse statistics to obscure the facts. To anyone who ever needed to learn the basics of statistics and probability theory and had trouble doing so --- i recommend this book without reservations. You can still find used copies for sale on the Web.

Joke remembered from “The Pocket Book of War Humour” (ed. Louis Untermeyer around 1943)

Officer getting off train, to Pullman porter: “What’s the average tip you get?”

Porter: “Two dollars, sir.”

(tip is disbursed)

Porter: “Thank you very much, sir! In thirty-five years, you’re the first traveller to come up to average!”

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Posted: 09 August 2007 07:44 AM   [ Ignore ]   [ # 7 ]
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I see what you mean and thanks. I used to proofread reports by Japanese irrigation engineers and they used the term “return period” which I think (this was a while ago) they used to refer to freak rainfall ie its highpoint and the time between this freak event and the next one which might be 70 years which screws up averages but which must be factored in for dam design.
The Indian Ocean tsunami defied all statistics because it was the first one there in recorded history so no averages or return periods were available I suppose (and this explains why there was no early warning system).

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Posted: 09 August 2007 07:53 AM   [ Ignore ]   [ # 8 ]
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venomousbede - 09 August 2007 07:44 AM

The Indian Ocean tsunami defied all statistics because it was the first one there in recorded history

Krakatoa?

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Posted: 09 August 2007 08:23 AM   [ Ignore ]   [ # 9 ]
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Krakatoa is in the Indian Ocean but it didn’t affect the areas the 2004 tsunami did so devastatingly because much of Sumatra was in the way and it was a lot further south. It did hit the Gulf of Thailand though on the other coast.
I could be wrong for a change in which case the return period would be 124 years.

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Posted: 09 August 2007 05:41 PM   [ Ignore ]   [ # 10 ]
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I’d just like to say that for me “on average” is perfectly acceptable in this context.  Certainly you can’t expect them to say, e.g., an average of 56.8375 volcanoes erupt every year.  As has been pointed out already it’s quite likely that there are years when there are more than 60 and years when there are less than 50.  And this was a documentary.  What was the target audience? If it were a scientific paper one might expect a more precise number, an explicit statement saying whether it was the arithmetic mean, the median, or the mode and what the standard deviation was, but for a documentary, where the likely audience was your average joe, “on average” sounds to me like a perfectly good term.

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Posted: 09 August 2007 08:33 PM   [ Ignore ]   [ # 11 ]
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If the commentator had simply said “there are usually between 50 and 60 eruptions in a year”, this thread would not have been started. The fact is that the statement, as made, caused doubt and confusion. “Average joe” hears/reads far too many such ambiguous statements every day; he/she deserves better. This one at least wasn’t made with intent to mislead, but most of them are.

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Posted: 09 August 2007 11:37 PM   [ Ignore ]   [ # 12 ]
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lionello - 09 August 2007 08:33 PM

If the commentator had simply said “there are usually between 50 and 60 eruptions in a year”, this thread would not have been started. The fact is that the statement, as made, caused doubt and confusion. “Average joe” hears/reads far too many such ambiguous statements every day; he/she deserves better. This one at least wasn’t made with intent to mislead, but most of them are.

I think the average joe would not have suffered any “doubt and confusion” after hearing the statement that prompted this thread. The ambiguity, if there is any, exists only for those who have an expectation of a precision in language that is unlikely to met by any except those expecting it.

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Posted: 10 August 2007 07:36 AM   [ Ignore ]   [ # 13 ]
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lionello - 09 August 2007 08:33 PM

If the commentator had simply said “there are usually between 50 and 60 eruptions in a year”, this thread would not have been started.

Then we would have been discussing what the heck does “usually” mean. 

IMO, saying “usually” is even less helpful than saying “the average is 55”.  By stating “the average”, at least you imply that there aren’t wild swings, i.e. it’s likely that there are between 0 and a few hundred per year. OTOH, “usually there are between 50 and 60” allows for “except for than one year when there were 2,349,310 eruptions”.

To be accurate, the announcer must give the mean, the standard deviation, the variance, the period, ... at which point 99% of the audience has switched over to “So You Think You Can Dance?”. (^_^)

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Posted: 10 August 2007 10:20 AM   [ Ignore ]   [ # 14 ]
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On average between 50 and 60 volcanoes erupt every year and Between 50 and 60 volcanoes erupt every year mean precisely the same thing, so “on average” is redundant.  I don’t buy the fact that the writer means that sometimes that average could be 41 or 78 in any one year.  I just think he’s being sloppy.  If you’re talking about averages, why not give a precise figure, eg On average 57.1 volcanoes erupt every year? 

How does .1 of a volcano erupt?  Just a teeny little pardon-me burp of an eruption or what?

Edit:  Why does Dr Techie have to go on holiday when we need him?
Quick second edit:  Not that I associate Dr Techie with burping, let alone excessive intake of alcohol, of course.  Perish the thought.

[ Edited: 10 August 2007 10:36 AM by ElizaD ]
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Posted: 10 August 2007 11:45 AM   [ Ignore ]   [ # 15 ]
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Might we also consider that the true average here is a moving target, that is to say, the average changes every year as the number of volcanoes erupting changes every year.  This is a documentary which may be shown for a number of years—with the average changing every year.  So, for the sake of the documentary’s accuracy year after year, such a statement makes sense.

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