As types of average (in the mathematical sense, excluding such non-mathematical uses as 'an average person') we've mentioned mean, median and mode.

Complicating it, there are other mathematical senses of 'average'. For example, one can take the geometric average of n numbers.¹

And what is your 'average' speed if you drive to your destination at 30 mph, and then return to your starting point (by the same route) at 60 mph? (Hint: the average speed is not 45 mph.) The sort of 'average' you're talking about here is called (I think) the harmonicc mean.

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¹ Multiply them together, and then take the nth root of the product.

Average has several meanings in the insurance industry.
In Marine insurance, ‘average’ means loss and ‘particular average’ means partial loss. See also ‘General Average’.
If a policy is ‘subject to average’, then, if the sum insured at the time of a loss is less than the actual value of the property insured, then the amount of claimed under the policy will be reduced in proportion to the underinsurance. In mathematical terms:

Allowable Claim =
Loss x Sum Insured

Value at risk

If you do not insure for the full values at risk, then you may not be able to obtain a full settlement of any loss. See also “First Loss”.
 

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And what is your 'average' speed if you drive to your destination at 30 mph, and then return to your starting point (by the same route) at 60 mph?

If your journey is 30 miles, then, making no allowance for turnaround, the journey out will take 1 hour and the journey back will take half an hour. Total 1.5 hours.

60 divided by 1.5 equals 40. Or that's what I reckon, anyway.

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Average has several meanings in the insurance industry

This used to cause all sorts of problems when people put in claims to my agency for partial loss of baggage. If their baggage was insured for, say, £300 and they lost one item - a designer item, say, that was valued at £250 - they couldn't see why their claim was reduced because of the average clause.

I used to say to them, "If you've got one item in your bag that's really expensive and worth £250 - how come everything else is of such poor quality and low value?" That used to do the trick!

A news item in the travel press today is interesting and relevant to the railways discussion.

'COMPETITION from high speed TGV trains could see Air France cut as much as 25% of its domestic workforce by 2016.

A statement issued by the carrier on Fri said “We expect that the competition with the TGV will increase, and we have informed the unions of our plans to adapt the organisation”.'

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Originally posted by Richard English:

quote:

And what is your 'average' speed if you drive to your destination at 30 mph, and then return to your starting point (by the same route) at 60 mph?

If your journey is 30 miles, then, making no allowance for turnaround, the journey out will take 1 hour and the journey back will take half an hour. Total 1.5 hours.

60 divided by 1.5 equals 40. Or that's what I reckon, anyway.

Yes. Expressed mathematically, what you've with the initial 30 and 60 mph is this:

1. Take the reciprocals: 1/30 and 1/60:
   
2. Figure their mean:
   half of (1/30 + 1/60) = half of (3/60) = half of (1/20) = 1/40
   
3. Take the reciprocal of that mean: reciprocal of (1/40) = 40

So the harmonic average is "the-reciprocal-of-the-(mean-of-the-reciprocals)".

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what is your 'average' speed if you drive to your destination at 30 mph, and then return to your starting point (by the same route) at 60 mph?

Note that the harmonic means method works because the distances traveled are equal and the times spent at each speed are not. You spend more time going 30 than 60, so the mean is closer to 30 than 60. If you drive 30 mph for an hour and then 60 mph for an hour, your mean velocity is 45 mph.

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'COMPETITION from high speed TGV trains could see Air France cut as much as 25% of its domestic workforce by 2016.

Sounds like they plan to shamelessly neglect some routes.

Hacking through statistics and train service, I revert to the initial theme of words-for-letters. As an exercise I once complied a list of the worst possible such words I could find. I invite this erudite group to improve upon it:

Aestivate
Bdelloid
Cephalopod, chanukah, chiaroscuro, chlamys, chthonian, cynosure, czar
Djbouti.
Ennui.
Fiscal
Gnome
Hanukkah
Introit
Jejune
Knight, knob
Lladro
Mnemosyne
Night, nob
Oenology
Phlegm, phthisis, pterodactyl
Quay
Retch
Sinecure, syzygy
Tsar, tsunami
Uxorious
Velleity
Wraith, wretch
Xylem
Ytterbium
Zymurgy, zygodactyl

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Sounds like they plan to shamelessly neglect some routes.

No doubt. But there is a massive difference between reducing an airline schedule between two points, which leaves the infrastructure completely unaffected, and closing a rail route with the attendant removal of the track, stations, bridges, cuttings, tunnels and all the other things that make up en-route rail infrastructure.

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But there is a massive difference between reducing an airline schedule between two points, which leaves the infrastructure completely unaffected, and closing a rail route with the attendant removal of the track, stations, bridges, cuttings, tunnels and all the other things that make up en-route rail infrastructure.

Precisely! That's why we prefer investment in air travel to more expensive high-maintenance Victorian technology.

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Precisely! That's why we prefer investment in air travel to more expensive high-maintenance Victorian technology.

All forms of transport have their advantages and disadvantages, costs being just one. Air travel is not necessarily cheaper than rail travel - or vices versa. It depends on many factors, including, but not limited to, distance, passenger numbers, topography and political situation.

For example, air routes are usually easier to set up, needing no track, but the cost of operating an aircraft is far higher per passenger mile than the cost of operating a train (or come to that, a 'bus). One flight from New York to Chicago will be much cheaper than one rail journey if you first have to lay the track. But once the track and infrastructure is installed, the variable costs of train operation are much lower and, eventually, once the initial building costs have been amortised, then the train will be cheaper to operate.