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I'm reading a novel set in the English war effort of WWII. The characters have an odd way of referring to time, as where as Colonel says, "There's a meeting later this morning. I have to get a briefing to the boss by nine ack emma. Hence the hurry."

Can someone explain?
 
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That's WW1 British military parlance for 'AM' (morning). See this Wikpedia entry.


Build a man a fire and he's warm for a day. Set a man on fire and he's warm for the rest of his life.
 
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WW1 and maybe earlier. By WW2 the forces had largely adopted the 24-hour clock, thus relegating ack emma and pip emma to the annuls of history where they rightly belong.


Richard English
 
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From the OED Online:

quote:
ack
and vars., used for a in the oral transliteration of code messages and in telephone communications, as in ack emma, for a.m. = ante meridiem; air mechanic. See ACK-ACK, EMMA. In military use replaced by able in Dec. 1942.

1898 Signalling Instructions (War Office) 86 The letters T, A, B, M,..will be called toc, ak [1904 Signalling Regs. ack], beer, emma. 1917 ‘IAN HAY’ Carrying On vi. 134 He [the Signaller] salutes the rosy dawn as ‘Akk Emma’, and eventide as ‘Pip Emma’. 1918 Signalling Simplified II Special Names of Letters. (Semaphore and Morse.) A = Ack...Note that, in signalling, these Special Names must always be used, i.e. A is always Ack, M is always Emma, and so on. 1927 D. L. SAYERS Unnatural Death III. xxiii. 285 Some damned thing at the Yard, I suppose. At three ack emma! 1930 BROPHY & PARTRIDGE Songs & Slang, 1914-18 93 Ack Emma, Air Mechanic, in the Royal Air Force. Also a.m. = morning. 1934 V. M. YEATES Winged Victory 78 The Ak Emma went off in search of food. a1935 T. E. LAWRENCE Mint (1955) xxii. 78 We shorten them [sc. our ranks] to LAC, AC I, AC II, and speak of ourselves as ‘ack-emmas’ (the air mechanic of the Great War) or ‘urks’.

emma
used orig. in telephone communications and in the oral transliteration of code messages, hence colloq., for m, as in ack emma, for a.m. (see ACK); emma-emma-esses (see quot. 1919); emma-gee, for m.g. = machine gun; pip emma, for p.m. (see PIP n.4); toc emma, for t.m. (see TOC EMMA).

1891 Man. Instructions Signalling 94 The reader may pronounce his letters in any distinctive method to distinguish those letters which resemble others in sound, e.g. B, V, D, E, or M, N, etc. may be called Beer, Vay, Do, E, and Emma and N, etc. 1898, etc. [see ACK]. 1915 ‘IAN HAY’ First Hundred Thousand xix. 289 ‘Pip Emma’{em}as our friends the ‘buzzers’ call the afternoon. 1918 H. W. MCBRIDE Emma Gees i. 9 Emma Gee is signaler's lingo for M.G., meaning machine gunner. 1919 DOWNING Digger Dialects 22 Emma-emma-esses, smoke-oh. (From the signal alphabet, MMS, Men may smoke.) 1926 E. WALLACE Door with Seven Locks xiii. 125 Tell him I want to raid Gallows Cottage, Gallows Hill, at eleven-fifteen pip-emma. 1931 Morning Post 20 Aug. 8/5 He was the only infantry officer..who had a good word for the Trench Mortar crowd. ‘Are you Toc Emmas? You're just the men I want.’ 1969 WODEHOUSE Pelican at Blandings vi. 83 We shall meet at twelve pip emma.
British signalman's letter code British signalman's letter code, from from Weird Words:

quote:
Ack
Beer
Charlie
Don
Edward
Freddie
Gee
Harry
Ink
Johnnie
King
London
Emma
Nuts
Oranges
Pip
Queen
Robert
Esses
Toc
Uncle
Vic
William
Xray
Yorker
Zebra
 
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I love those code words, Tinman. They remind me of airlines and others who use words for the letters, such as "gate charlie." I know we've talked about that before, but I am always surprised by the words they use to represent letters. And I am surprised with these code words, too. I especially like "emma" for "m."
 
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Charlie is the only one of two of those old codes that carried forward to the new international codes. Indeed, it is one of only six people's names to be in the current international list, which is:

Alpha
Bravo
Charlie
Delta
Echo
Foxtrot
Golf
Hotel
India
Juliet
Kilo
Lima
Mike
November
Oscar
Papa
Quebec
Romeo
Sierra
Tango
Uniform
Victor
Whisky
X-ray
Yankee
Zulu

I use these names without thinking as they are universal in the travel industry, so, if I were spelling a name to a carrier, I would simply say something like, "That's kilo-alpha=lima-lima-hotel". But, interestingly, when I came to write the list out I had to go through the alphabet letter by letter to recall what each was!

The old list, that Kalleh so likes, has much charm but wouldn't be recognised all that well nowadays. The international list is supposed to comprise words that are easy to pronounce regardless of the speaker's nationality, commonly used and understood in many languages and difficult to confuse one with another - as could, say, M for mut and n for nut. Learning the correct list and committing it to memory will help those occasions when you are asked to spell a word and just can't think of an exemplar use - leading to such solecisms as "That's F for, err, for, err, for, for - effervescence".

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Richard English
 
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"That's F for, err, for, err, for, for - effervescence".


F for Freddie sounds really familiar. Why is that?
 
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F for Freddie sounds really familiar. Why is that?

Because it was the old British telephonic code as exemplified earlier.


Richard English
 
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As a newspaper editor, I sometimes find the military alphabet or something close to it is handy in making sure that I get or relay spellings correctly.
Given the incredible number of ways there are to spell some first names these days, I always check for how this particular person spells, for instance, Crystal, or Krystal, or Krystelle, or ...
 
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F for Freddie sounds really familiar. Why is that?

Perhaps you remember it from the movie Target For Tonight.
 
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Welcome, Verbivore! See your PM.
 
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As a newspaper editor, I sometimes find the military alphabet or something close to it is handy in making sure that I get or relay spellings correctly.

It's interesting that you call it the "military alphabet". I recall recently during a discussion on the 24-hour clock, that Kalleh referred to that as "military time".

Is it common in North America to refer to these international standards as "military"? Of course, the military always use them but then so do those working in transport, the police and others in organisations where ambiguity must always be avoided.


Richard English
 
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Richard:
I have heard a lot of people in Canada refer to the 24-hour clock as military time.
I think the military were probably the first to use it, and a lot of other groups realized it made sense in their jobs as well, so they picked it up.
It's interesting that even though most people now hear about it in connction with police work, it's still associated more with the military.
 
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The research I have done seems to show that it is the USA and Canada where the expression "military time" is used to denote the 24-hour clock.

Which group was the first to adopt the 24 hour clock I don't know and haven't yet been able to find out. Certainly it was the standard in the travel industry when I started in it in 1960.


Richard English
 
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Of course, there are differences of opinion about how to refer to the 24-hour clock. One of my friends calls it "railway time".
The fact that he has worked for CN Rail for more than 30 years is, I'm sure, just a coincidence.
 
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When the railways were invented, it soon became clear that a better method of deciding on time was needed than that commonly adopted in the early 19th century - simply checking when the sun was at its height and calling that 1200. Even in a country as small as England, there can be difference of 20 minutes of sun time or so between locations. This didn't matter too much when it took a couple of days to get from London to Bristol - but then The Great Western Railway was covering the distance in less than three hours, it became a problem if the Bristol guard's watch showed a time that was 20 minutes later than the London signalman's watch.

So the railways agreed that they would all use the same time for their operations and timetables, and that the clocks on railway stations would show that standard time - which quickly became known as "railway time". Railway times and local times existed side-by-side for many years and it was not until the end of the 19th century that the idea of standardised time zones, based on the meridians of longitude, was finally put in place. Although the conference that decided this took place in Canada, the zero meridian, from which all other were enumerated and thus from which all time started, was set in London (or to be exact, Greenwich).

All transport undertakings had to adopt some kind of standard and most adopted local times, based on a set deviation from Greenwich time. But when I started in travel, Russian railways had their own system - all trains in Russia ran to Moscow time - which was eight hours behind Siberia time!

New international standards for time designation have been agreed and accepted by most countries, including the USA, but I doubt that I shall see their general acceptance even in the UK, let alone the USA, so reluctant are people to change from their own norms. Wikipedia has a good article http://en.wikipedia.org/wiki/Date_and_time_notation_by_country


Richard English
 
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quote:
Originally posted by Richard English:
When the railways were invented, it soon became clear that a better method of deciding on time was needed than that commonly adopted in the early 19th century... and it was not until the end of the 19th century that the idea of standardised time zones, based on the meridians of longitude, was finally put in place. Although the conference that decided this took place in Canada...


Actually, the conference was held in Washington D.C. The Canadian connection was that the whole proposal for standardized time zones was the brainchild of the great Canadian railway engineer Sir Sandford Fleming. He promoted the idea for many years against the most stubborn opposition and was finally successful in 1885. If the time discrepancy on English railroads was noticeable, imagine that between Halifax, Nova Scotia and Victoria, British Columbia. It's not surprising that a Canadian came up with the solution.
 
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Apologies. I quoted all this from memory and I thought that the conference, as well as the idea, was Canadian.

And I agree that it was long-distance high-speed travel that really provided the impetus for a proper standardised system.

And, as an aside, isn't it a shame that the once-great Canadian railway system, built at such huge cost in the face of massive geographical and geological difficulties, is now almost extinct.

The old mining town of Hedley, which I shall be visiting in May, used to be served by its own railway that connected it with both Vancouver and the USA and, just down the road, Pentiction was served by the wonderful, and wonderfully-named, Kettle Valley Railroad. In Britain we got rid of far too many of our railways; the USA got rid of even more of theirs - but Canada ripped theirs up in a wholesale orgy of destruction which I am sure many Canadians now regret.


Richard English
 
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I've trotted this out before when this subject has come up, but if I don't publicise my own site nobody else will! See my article on Greenwich Guide.


Build a man a fire and he's warm for a day. Set a man on fire and he's warm for the rest of his life.
 
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quote:
Originally posted by Richard English:

And, as an aside, isn't it a shame that the once-great Canadian railway system, built at such huge cost in the face of massive geographical and geological difficulties, is now almost extinct.


I would add to that, political and economic difficulties. Railway building in Canada brought down and almost bankrupted governments, both federal and provincial. Having a railway in the 19th century was the thing to do. Without a railway you were considered by others and by yourself as being backward. But, the building of the Canadian Pacific Railway ranks right up there with the Battle of Vimy Ridge (WWI)as a defining and unifying moment in Canadian history.
However, I would not write off the railways of this country just yet. Railways are extremely efficient at moving large volumes long distances. Canada has both of those! As long as the world wants our wheat and potash and iron ore, we'll have to get those commodities down to tidewater. Railways still do that best.
 
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I think passenger rail travel declined in Canada for the same reason it declined in the U.S.: people stopped taking the train, because they preferred the alternatives. One still has the option of taking the train from San Francisco to Chicago if one wishes, but nobody does it because it's more expensive, less convenient and takes three days.
 
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I agree with most of what you both say. Rail travel is a very efficient way of moving large volumes long distances and it would be wonderful right now in Canada. But Canada now has relatively few railways left to do the job, as most of them were ripped up in the middle of the last century. Had the rail companies simply closed the lines that wouldn't have been so bad - but in Canada, as in other countries, they took up the metals and sold off the land. No chance, once that's been done, of reopening the line.

In the middle of the last century rail travel declined against the competition of air and road. But that is changing. Both road and air travel has become slower and more troublesome and rail (in most countries) quicker and more comfortable. Few people now fly between London and any of the cities within 300 miles; it's as quick to take the train and a lot less stressful.

Even in the USA, where the railways have been shamefully neglected, a surprising number still prefer to travel by rail, in spite of the low average speeds occasioned by the sad state of the permanent way. Last year I travelled from Chicago to Seattle and back by train and will be doing the same this year. The journey was slow, taking two days each way, I accept (although if The Empire Builder travelled at the speed of the best European trains it would take only around half that time) but that was two days of great comfort and the fare (lower, not higher, than the air fare) included in that two days, six meals at a proper table with a proper tablecloth and waiter service, plus two night's sleeping accommodation. Not for everyone, I agree, but there were plenty on the train that I took, to whom comfort and a stress-free journey meant more than speed.

Rail passenger numbers in the UK are now back to the levels of 1947 - and would be higher had not so many lines been closed. Indeed, such is the demand, that new lines are being built and our first dedicated high-speed line (which means speeds of around 180 mph) has just been opened to reduce the journey time from central London to central Paris or Brussels to around 2 hours. Impossible to do that journey more quickly by any other means.


Richard English
 
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(although if The Empire Builder travelled at the speed of the best European trains it would take only around half that time)

It's one thing to build a high-speed line from Paris to Lyon, but another thing entirely to build one from Chicago to Seattle. I doubt that even the best European trains could cross the Rockies at the speed of the best European trains.

Don't get me wrong -- I like trains. I'd rather take trains around Europe than fly or drive. And air travel seems to suck more with each passing day. But Europe is made for trains in a way that the U.S. and Canada aren't. Railways in the US weren't neglected, they were bankrupted because not enough people were using them to pay the bills, which included enormous legacy and maintenance costs (hence the sad state of the permanent way).

I congratulate you finding an Amtrak fare lower than the lowest airfare; I've never been able to do it. The Amtrak SF-Chicago fare is about $300 round trip (airfare is about $250), but that only gets you a coach seat. Including meals and bed brings it up $800. True, you save the cost of a hotel and meals, but, comfortable and stress-free as it may be, it's still a hotel that you can't leave for four days. Air travel still has some room to deteriorate further before the California Zephyr becomes an attractive alternative for the vast majority of travellers.
 
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But Europe is made for trains in a way that the U.S. and Canada aren't. Railways in the US weren't neglected, they were bankrupted because not enough people were using them to pay the bills, which included enormous legacy and maintenance costs (hence the sad state of the permanent way).

At one time the railways in the USA were far BETTER than most of those in Europe. But they went bankrupt because they didn't receive sufficient Government support. The need for support for the railways is the case for all the world's railways - none have been self-financing for around a century.

Most countries realised this and invested in their railways - although it is strange that most Governments seem to consider that money spent on the railways is "subsidy" whereas the (far greater) sums of money spent on the roads is "investment".

Although it would be difficult to have a high-speed line through the Rockies, that part of the transcontinental journey is only around 10% of the distance. And even there the trackbed alignment is actually quite good on the Empire Builder route - it is the shocking state of the metals that means that the end to end average speed is a paltry 50 mph and far less in the Rockies section. It would be relatively easy to construct a high speed line across most of the USA - much of which is completely empty apart from fields of grain. Very different from most of Europe which is highly built up - especially the UK where our latest high-speed line was built through London and Kent - two of the most highly urbanised areas in the world.

In the USA it is the will that is lacking, not the money or the ability. The country that was building Liberty Ships at the rate of one a week in the 1940s could certainly build a simple thing like a high-speed railway line if it wanted to.


Richard English
 
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The country that was building Liberty Ships at the rate of one a week in the 1940s could certainly build a simple thing like a high-speed railway line if it wanted to.

Precisely. We don't want to. My objection is to your characterization of the railways as "shamelessly neglected". They didn't go under because people got lazy and forgot about them. My backyard is shamelessly neglected; the passenger railways were actively and intentionally retired, with virtually no political objection, and what little survives does so because of government subsidies. Good or bad, it was a conscious decision.
 
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Sometimes I feel as though I am watching "Groundhog Day" here... Wink
 
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My objection is to your characterization of the railways as "shamelessly neglected". They didn't go under because people got lazy and forgot about them.

Shameless neglect doesn't have to be unconscious - indeed it is often, as is doubtless the case with your back yard, quite conscious.

Railways, throughout the world, survive because of Government subsidies. Just as do roads. The US Government rook the decision to let its railways die and spent money on roads - as did many other Governments, including ours. Those that continued to invest in their railways - the Swiss, for example - are now blessed with excellent and modern rail systems that are of great value to their transport infrastructure.

Those Governments that did neglect their railways are, in the main, realising their mistake and trying to put it right. As fossil fuels get scarcer and more expensive, railways will become ever more important as a transport system. Remember, unlike any other form of transport yet invented, rail vehicles can run for unlimited distances, at very high speeds, on electricity - which can be produced by renewable sources.

Sooner or later the US Government will realise the importance of its rail infrastructure and then we will see a rapid re-birth of the system. But that will require the will of the Government - and at the moment its efforts are concentrated on other things.


Richard English
 
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On the when-you're-handed-a-lemon-make-lemonade theory, we turned our local abandoned railbed into a 900 kilometer public hiking/snowmobiling trail and nostalgically called it the Trailway. Smile
 
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So, Kalleh, you just came out to San Francisco on business. How subsidized would the train have to be before you would have considered spending, say, 36 hrs in a train rather than 12 hours in a plane?
 
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But Europe is made for trains in a way that the U.S. and Canada aren't. Railways in the US weren't neglected, they were bankrupted because not enough people were using them to pay the bills, which included enormous legacy and maintenance costs (hence the sad state of the permanent way).
I was very interested in neveu's analysis of the reason passenger railways aren't as popular as they are in other countries. While we've often discussed the subject of the U.S.'s "shameful" treatment of the railways, courtesy of Richard, I've never heard the other side articulated as well as neveu did here. I think neveu is right. Railways just aren't the answer to transportation in the U.S. as they are in other countries. This is not a one-size-fits-all world, unfortunately. Now, we must do something about our use of fossil fuels, I agree. But I don't see that railways are the answer to that.
quote:
How subsidized would the train have to be before you would have considered spending, say, 36 hrs in a train rather than 12 hours in a plane?
Timewise, I couldn't have done it. Period. Had it been a vacation, and not a work trip, I suppose I could have. However, it would have taken about 2 days away from my time spent in SF, so I still wouldn't have chosen to do that.
 
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As usual, Richard has prompted me to try to actually back up my table-pounding with numbers. Here is the website for the Bureau of Transportation Statistics, U.S. Department of Transportation. Here are a few highlights and a little analysis. Units are in million (1,000,000) passenger miles.

The total number of passenger miles 2005: 5,523,307
Highway miles, 2005: 4,884,557 (88.4%)
Air miles, 2005: 583,689 (10.6%)
Mass transit, including bus: 49,680 (00.9%)
Rail, inter-city, Amtrak 5,381 (00.1%)

What surprised me what how quickly the railroads collapsed. Even in 1960, the year the 707 was introduced, air passenger-miles were nearly double rail passenger-miles.

Finally, the average distance traveled by an American in a year is 18341.33 miles, give Americans a mean velocity of 18341 miles per year, or 2.09 miles per hour.
I will leave calculating the mean velocity of a Brit as an exercise for the interested reader.

[Addendum: More Number Fun!]
The average American flew about 2000 miles in 2005. Assuming the mean velocity of a plane trip is about 500 miles per hour, the average time spent in a plane was about 4 hours. Which means that at any given moment, about a 130,000 Americans are in the air. And that the mean altitude of an American is 13 ft.

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By coincidence, this week's Time magazine has an article on India's railway system and that has some interesting comparative statistics. It quotes Railway Gazette International as its source (a respected publication) but I have not cross-checked them myself.

They do not quote UK figures but I might try to source them myself - they shouldn't be hard to find. But these are their comparison:

Route mileage: USA 96,000; India; 39,000; France 18,000; Japan 12,000
Annual passengers: Japan 8.68 billion; India 5.38 billion; USA 3.16 billion; France 960 million
Average speed of the fastest train: France 173mph; Japan 159mph; USA 100mph; India 62mph.

I was unsurprised by track mileage figures since the USA is so much larger than the other countries - although I wonder how much of that track mileage is used intensively. But the USA's annual passenger carryings was a surprise - although most of those passengers will be urban commuters, I imagine. I don't know which US rail route offers the 100mph service; the Empire Builder has an end to end average of half that.


Richard English
 
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quote:
And that the mean altitude of an American is 13 ft.

The mean or the average? I suspect the latter.


Richard English
 
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In the way that you mean "average" it is exactly the same as the mean (the sum of all the values divided by how many values there are).

Neither of the other two common "averages" - the median and the mode - would give anything like 13 ft as an answer. The mode (the most common value) would certainly be zero as more people are on the ground than at any other single altitude at any given time. The median is the central value i.e halfway between the lowest and highest values and would be half the highest altitude for a plane and I suspect that's a good deal more than 13 ft.

The original statement was therefore mathematically correct.
 
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Maybe I was using the wrong terms. I had always understood the average to be the sum of all the values divided by how many values there are, and the mean to be the point at which most of the values were - possibly the mid-point. But maybe I should have used a different term (mode, maybe?).

For example, I had always understood that the average number of legs in the human population was about 1.999 but the mean (the number that most people have) is 2.


Richard English
 
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No. The mean is what most people understand as the "average" - the sum of the values divided by the number of values. The mode is, as Bob says, the most common value. In your example of legs, it would be 2, whereas the mean would be perhaps 1.999... Finally, the other average is the median; the figure midway between the highest and lowest. 50% have a higher figure and 50% have a lower. Since there are some people with no legs and some with one, but the vast majority have two, the figure in this case would be perhaps 1.999...


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And of course the MODE doesnt have to be single valued. For example in the following set of numbers 3 and 5 are both modes because each occurs three times and no other number occurs more than twice.

1 2 2 3 3 3 4 5 5 5 7 8 8
 
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Of course we could alwas calculate the root mean square (or even the cube root mean cube) and the standard deviation but frankly people round here may think of standard deviation in other terms. Red Face
 
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quote:
...at any given moment, about a 130,000 Americans are in the air.

My adviser used to put this as a puzzle to his new grad students: how many Americans are living at an altitude of 30,000 feet or more?

quote:
I don't know which US rail route offers the 100mph service

The Acela Express. Includes an interesting summary of passenger rail in the US.

quote:
although I wonder how much of that track mileage is used intensively

I believe that US railroads still haul quite a bit of freight. It's passenger service that has nearly vanished from much of the country

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Neither of the other two common "averages" - the median and the mode
I always thought the "average" was only the "mean." Is that not correct?
 
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I always thought the "average" was only the "mean." Is that not correct?

As with many words, average has different meanings. When used in a strictly mathematical sense, it is as Bob and Arnie have said. When used in a colloquial sense (like when suck means sub-optimal), it has another. Most word-loving folk have moved beyond the one-word-one-meaning belief system. Your mileage may vary.


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Thank you for the explanation. So in my example, the average, or the mean, number of legs is around 1.999 whereas the median number is 2. Have I got that right?

I use this example in a training exercise so it's important that I am accurate.


Richard English
 
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The Acela Express. Includes an interesting summary of passenger rail in the US.

The example here is typical of what is happening in the rest of the world where investment is made in railways. Even though the Acela is significantly slower that most European high speed lines, and the distance of 456 miles significantly greater than the average distance between cities in Europe, it has already captured over 50% of the "market share" on the route. It is not clear whether that market share includes private motorists or whether it is only public transport. But either way it is significant.

Incidentally, tilting train technology is not new; the first such train in public service, so far as I know, was the British APT, designed and built in Derby in 1979 - nearly 30 years ago. http://www.apt-p.com/aptintroduction.htm Sadly our Government, which at that time owned our railways, was not prepared to invest the money needed to develop the prototype and, after a year, it was withdrawn from service and now languishing in a siding at Crewe, where those passengers whizzing past in one of Virgin's tilting Pendolinos (built in Italy) are, in the main, quite unaware that this sad-looking train was the inspiration for the one in which they are travelling. The Italians had the foresight that we lacked.


Richard English
 
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the average, or the mean, number of legs is around 1.999 whereas the median number is 2. Have I got that right?
The mode would be 2 (the most common number). The mean and the median would both be around 1.999... They'd probably be slightly different though if calculated out to umpteen decimal places.


Build a man a fire and he's warm for a day. Set a man on fire and he's warm for the rest of his life.
 
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The mean and the median would both be around 1.999

No, I think the median would 2.
The median is the value m such that half the samples are greater than or equal to m and half are less than or equal to m.

If the sample size is an odd number then it is just the "center" value, in this case 2:
(0, 0, 1, 2, 2, 2, 2)

If the sample size is even, e.g.
(0, 0, 1, 1, 1, 2 \\ 2, 2, 2, 2, 2, 2)

the median would fall where I placed the slashes and would be 2.

If the sample is
(0, 0, 0, 1, 1, 1, \\ 2, 2, 2, 2, 2, 2,)

the median is customarily taken as the mean of the two numbers on each side (1, 2) and would be 1.5

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As with many words, average has different meanings. When used in a strictly mathematical sense, it is as Bob and Arnie have said. When used in a colloquial sense (like when suck means sub-optimal), it has another. Most word-loving folk have moved beyond the one-word-one-meaning belief system. Your mileage may vary.
Yes, z, I understand that words can have more than one definition. Having posted here for 5 1/2 years, I'd better! However, here is what Bob said about the average:
quote:
Neither of the other two common "averages" - the median and the mode...."
He considers the "mean," the "mode," and the "median" to be synonymous with "average." I don't. I think only "mean" is synonymous with average. However, after I read Bob's post, I thought maybe that was an American/British difference. Yet arnie said:
quote:
The mean is what most people understand as the "average" - the sum of the values divided by the number of values.
That was what I'd learned the arithmetic definition of "average" to mean.

So then I looked it up, which, of course, is what I should have done in the first place. Here is the definition, related to the arithmetic definition of "average," from some of the online dictionaries:

Random House - "Statistics. arithmetic mean."
AHD - "The value obtained by dividing the sum of a set of quantities by the number of quantities in the set. Also called average." and "See arithmetic mean."
Wordnet - "5. relating to or constituting the most frequent value in a distribution; 'the modal age at which American novelists reach their peak is 30' [syn: modal]
6. relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values); "the median value of 17, 20, and 36 is 20'; 'the median income for the year was $15,000' [syn: median]"
Kernerman English Multilingual Dictionary - "the result of adding several amounts together and dividing the total by the number of amounts
Example: The average of 3, 7, 9 and 13 is 8 (= 32:4)."
COED - "the result obtained by adding several amounts together and then dividing the total by the number of amounts."
Merriam-Webster's - "synonyms average, mean, median, norm mean something that represents a middle point.
OED - N "6. a. The arithmetical mean so obtained; the medium amount, the generally prevailing, or ruling, quantity, rate, or degree; the ‘common run.’" and V "1. trans. To estimate, by dividing the aggregate of a series by the number of its units, (at so much); to take the average of; to form an opinion as to the prevailing standard of."

In summary, Wordnet and the online Merriam-Webster's cites the "mode" and "median" as definitions of "average." Wordnet doesn't cite "mean" at all, though MW cites "mean," median," and mode." Of the online dictionaries I accessed, the Merriam-Webster's online and Wordnet agree with Bob on his definition of "average." The rest define it as "mean."

Bottom line, I think it would be confusing to many to use the word "average" for a "mode" or "median."
 
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Which is why the common usage is to treat "average" as synonymous with "mean". That however is not the mathematical usage and I am after all, by training, a mathematician.
 
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Of course, there is more than one type of mean. The Wikipedia page lists quite a few, in addition to the standard mean(arithmetic), the common geometric and harmonic means, I count about 27 more.

As Wikipedia says, average also refers to the expected value of a random variable, although typically this will be the same as the mean of the values, with some fanciness for infinite distributions. For example, the expected value of a bell curve (normal distribution) centered at 0 is clearly 0, but it isn't really a mean.

It is a testament to the strange language of mathematicians that a random variable is neither random, nor a variable, and it's expected value can be a value you never expect to occur. For example, a throw of a die is a random variable, and the expected number of spots for a six-sided die is 3.5, which is unlikely to occur on any given roll.
 
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Which is why the common usage is to treat "average" as synonymous with "mean". That however is not the mathematical usage and I am after all, by training, a mathematician.
I am surprised that mathematicians use the word "average," as it is so imprecise. I have been educated in statistics, as a researcher, and I've not seen the term "average" used in a research report. "Average," at least in statistical mathematics, is considered a layman's term.

Of course, I suppose somewhere in some scientific report one could find the word "average," but it certainly isn't common.
 
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Many people treat the word "average" as a synonym for "normal" or "ordinary" in their common sense. "He's and average kind of guy" means that he behaves much as do other guys. But he might not be average in any mathematical sense at all.

The word itself has many meanings, some of them very precise - but in the way I've exemplified above it is very vague.


Richard English
 
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