Calculating Average Fuel Consumption

**windsock** · 19th June 2010, 09:05 AM

Originally Posted by vnx205

The figure of 12 litres/100 km for the first 300 km of the trip is an average for the first 300 km. It is an average, because that is how the figure is calculated. All the driver knows is that she used 36 litres to cover the 300 km, so she calculated from those two figures that the average for that part of the trip was 12 litres/100 km.

It might not be labelled as an average, but it definitely is an average.
I am using average in the colloquial sense. It is really the mean, but I am continuing the terminology used by the OP in the hope of avoiding confusion,

Does that help?

An average, or arithmatic mean (AM) value of something is the sum of all the samples divided by the sample size.

We do not end up doing that here.

Here the figures we end up with are distance, and fuel consumption rate. We end up with an overall rate of consumption, i.e. we are dividing the fuel consumed by the distance travelled, multiplying this to get a rate of consumption - xxlitres per 100km. Two distinct values from two different samples - distance travelled and fuel consumed. It is a rate of consumption, not an average by any mathematical definition I know of.

However, if we were to sample the fuel consumption by the metre each and every metre travelled and then averaged this at the end of the trip (based on the number of samples only) it would indeed be the average but in this case there is no indication of this being done and we only have final fuel consumption rates for each leg of the trip.

Pedantic I know but given the wording of the OP... it leaves a lot of doubt over what was required and indeed leaves open the misuse of an oft misused word.

**RoverP6B** · 19th June 2010, 09:13 AM

I tried to word my initial question as simply as possible so as to minimise the possibility of any misunderstandings, maybe I could have made it clearer.

In any case, I do seem to recall a number of people with posts being very critical of me, funny thing is that some of those posts have since disappeared.

As vnx205 clearly explained, the answer, the only answer which make any logical and mathematical sense is 11.7l/100km.

The reason is that the distances covered over each segment of the journey are not equal, and as such carry a different weighting within the total distance covered. Therefore the fuel consumed for each segment is also weighted differently and as such to simply add each fuel consumption figure and divide by 4 as was suggested by a few posters is simply incorrect.

Some who posted criticism have shown that they don't fully understand how to calculate fuel consumption figures for a trip, so I hope that they may now have learnt something, afterall life is all about learning and sharing,..isn't it?

Ron.

**vnx205** · 19th June 2010, 09:20 AM

Originally Posted by windsock

Pedantic I know but given the wording of the OP... it leaves a lot of doubt over what was required and indeed leaves open the misuse of an oft misused word.

That is only true if you think the OP was asking for something that is a mathematical nonsense.

I began with the assumption that he was interested in an answer that actually meant something.

Since he began by saying, " As with all things mathematical, there is only one correct answer, so what do you think?", there was no reason to assume that he wanted a mathematically meaningless answer.

**windsock** · 19th June 2010, 09:30 AM

Originally Posted by RoverP6B

I tried to word my initial question as simply as possible so as to minimise the possibility of any misunderstandings, maybe I could have made it clearer.

Yes, clarity would have assisted greatly. You were after "overall" not average if 11.7 is the correct answer

Originally Posted by RoverP6B

In any case, I do seem to recall a number of people with posts being very critical of me, funny thing is that some of those posts have since disappeared.

Moderated and rightly so

Originally Posted by RoverP6B

As vnx205 clearly explained, the answer, the only answer which make any logical and mathematical sense is 11.7l/100km.

The reason is that the distances covered over each segment of the journey are not equal, and as such carry a different weighting within the total distance covered. Therefore the fuel consumed for each segment is also weighted differently and as such to simply add each fuel consumption figure and divide by 4 as was suggested by a few posters is simply incorrect.

OK, I understand your explanation about the weighting bit fine. It does indeed make sense now I think about it. Thank you for the clarity of explanation.

I don't think it was ever explained previously about the weightings of the distances. I am glad it had nothing to do with averaging averages...

Originally Posted by RoverP6B

...I hope that they may now have learnt something, afterall life is all about learning and sharing,..isn't it?

Yes, it is no good getting older, unless you get wiser.

**windsock** · 19th June 2010, 09:32 AM

Originally Posted by vnx205

That is only true if you think the OP was asking for something that is a mathematical nonsense.

I began with the assumption that he was interested in an answer that actually meant something.

Since he began by saying, " As with all things mathematical, there is only one correct answer, so what do you think?", there was no reason to assume that he wanted a mathematically meaningless answer.

Being mathematically correct does not include dividing stuff and calling it a mean or average. The division of fuel consumed by distance is not mathematically an average but rather a rate.

**vnx205** · 19th June 2010, 09:44 AM

Originally Posted by windsock

.. ... .. ...
. I am glad it had nothing to do with averaging averages...

.. ... ....
.

If you read the rest of your Wikipedia page, you might change your mind.

**Landy Smurf** · 19th June 2010, 09:45 AM

Originally Posted by windsock

Yes, clarity would have assisted greatly. You were after "overall" not average if 11.7 is the correct answer

Moderated and rightly so

OK, I understand your explanation about the weighting bit fine. It does indeed make sense now I think about it. Thank you for the clarity of explanation.

I don't think it was ever explained previously about the weightings of the distances. I am glad it had nothing to do with averaging averages...

Yes, it is no good getting older, unless you get wiser.

i totally agree with everything you said throughout this thread

**windsock** · 19th June 2010, 09:54 AM

Originally Posted by vnx205

If you read the rest of your Wikipedia page, you might change your mind.

Go onnn... give us a clue what you are referring to... I didn't see anything remotely relevant to this thread... other than the formula showing how an average (or arithmatical mean) is calculated.

Always willing to learn.

**vnx205** · 19th June 2010, 10:01 AM

Originally Posted by windsock

Go onnn... give us a clue what you are referring to... I didn't see anything remotely relevant to this thread... other than the formula showing how an average (or arithmatical mean) is calculated.

Always willing to learn.

From your Wiki page:

In mathematics, an average, central tendency[1] of a data set is a measure of the "middle" or "expected" value of the data set.

An average is a single value that is meant to typify a list of values.

The concept of an average can be applied to a stream of data as well as a bounded set.

From [ame=http://en.wikipedia.org/wiki/Average]Average - Wikipedia, the free encyclopedia[/ame]

Just in case we are looking at different pages.

**windsock** · 19th June 2010, 10:11 AM

Originally Posted by vnx205

From your Wiki page:

In mathematics, an average, central tendency[1] of a data set is a measure of the "middle" or "expected" value of the data set.

An average is a single value that is meant to typify a list of values.

The concept of an average can be applied to a stream of data as well as a bounded set.

From Average - Wikipedia, the free encyclopedia

Just in case we are looking at different pages.

Yep, certainly on the same page, literally, but certainly not figuratively.

It was espoused on this thread multiple times that the calculation to get 12.5 was an average of averages. It is not so. It is an average of the rates of consumption as given. This is not the correct answer apparently as the OP has indicated that the weighting of the distances throws this out.

You have not indicated to me that you are correct in assuming 12.5 is derived from averaging the averages.

Infact, this whole exercise does not require averaging in any way form or other. It is a division exercise aimed at obtaining an overall rate.

Got me laughing though. There is something surreal about disagreements on the internet...

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