What is the realistic accuracy & precision of typical consumer MPG calculations (tripmeter miles/pump gallons)

Mad Roger wrote on 7/22/2017 7:42 PM:

I've never seen a trip odometer that didn't have tenths of a mile.

Only because averages don't impact the effect of limited accuracy, averaging mitigates the effect of limited precision. But both precision and accuracy impact the error in any one reading.

I think you are missing something. What you replied do does not in any way indicate a limited understanding of precision and accuracy. But affect each measurement taken. An inspection measurement will require the combination of accuracy and precision in that measurement be within some limit. What do you expect them to do, take dozens of measurements? There are economic considerations, especially since this is about economics anyway. It is to prevent excess profits from being made by shortchanging the customers.

Not sure what that means. What I am doing by repeatedly topping off is to reach the point where the fuel in the filler neck is right at the nozzle so it won't run anymore, but rather cuts off immediately. This results in a very consistent fill level.

I think my consistent mileage measurements support my conclusions.

You seem to be doubting my results. Are you suggesting I am fudging my data?

You seem obsessed with evaluating the resulting MPG measurement even though you can't put numbers on the accuracy of the parameters that impact the MPG errors. If you can't come up with numbers, your ideas are of no value. But that doesn't mean the errors in my MPG measurements aren't as they appear to be.
Actually, I do have numbers for the parameters. I know the mileage to a fraction of a mile (even though a tenth mile out of 400 is far more accurate than anything else involved) and I have no reason to doubt the pump giving me 20.0 gal when it says 20.0 gal. I don't fill up at the same pump each time so if some were off it would show up and I'd be able to identify which pumps were inaccurate.

You keep saying this without indicating what you mean.

Lol! You see, I understand you because you're the type of person I had in mind when I made that comment.

Have done, 0.1 mile over 100 miles has been calibrated... actually, it was much better than 0.1 mile since I can interpolate the analog dial. I don't drive that stretch of road anymore, so I can't calibrate 100.0 miles continuously anymore or I would.

Sorry, your sentence doesn't make sense to me. Can you construct it properly?

If what you say is true, why is it I have only seen 21 mpg a very, very few times in the 20 years I have been checking my mileage? If what you are saying is true, I should see a much wider variation in measurements than I see. As I have said, 95% of the time I get between 19.5 and 20.5 mpg or within a 4% range (+-2%). It's actually even tighter than that. It's more like 19.7 to 20.2 mpg but I can't say just how often.
--

Rick C

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On Fri, 21 Jul 2017 18:39:37 -0400, rickman wrote:

I don't think I've ever seen a gas station on a slope. However ... The errors in the calculation stem from errors that nobody seems to know what they are, which means nobody knows what they're talking about.
Assuming the tripmeter/pumpmeter calcultion is the method used, + A tripmeter of 300 miles is neither accurate nor precise + A pumpmeter of 20.25 gallons is likely relatively accurate & precise + Matching fuel level in the tank isn't even close to accurate nor precise
Any one measurement (either miles or gallons alone) can only be as accurate and precise as the worst measurement, while the miles/gallons calculation compounds those inaccuracies and imprecisions (in loss of sig figs).
I think most of us would probably assume the pumpmeter is the most accurate and the most precise, but the other two measurements aren't even close to accurate or precise.
What matters is how accurate & precise is a 300 mile tripmeter reading? And how accurate and precise is the match to the previous fuel level?
I posit that the best you can do, overall, after running the calculation, is something like plus or minus about 1 mile per gallon such that 20 mpg is actually anywhere from 19 to 21 miles per gallon actual.
What I'm seeking is data that tells us the three main questions that must be answered for anyone to say that my hypothesis is even close to being right or wrong:
+ How accurate & precise is a reading of 300 miles on a typical tripmeter? + How accurate & precise is a reading of 20.25 gallons on a gas pump? + How accurate & precise is the matching of the prior fuel level done?
No calculation can do better than the worst measurement, and worse, errors compound when you multiply or divide.

But that's the kind of things we're looking for, which is why the minimum number of calculations possible is two, since you have to have a "before" situation and an "after" situation.
For example, if the change that you are testing causes about 1 mile per gallon decrease in fuel economy overall (but which isn't linear), but if your calculations are no better than plus or minus 1 mile per gallon in accuracy or precision, then you'll never even see the very real difference because it will be unmeasurable given the plus or minus 1 mile per gallon typical accuracy and precision that I posit the typical mom-and-pop tripmeter/pumpmeter calculation provides.
But there's no sense in talking about *any* of that, if we don't know the answer to these three questions. + How accurate & precise is a reading of 300 miles on a typical tripmeter? + How accurate & precise is a reading of 20.25 gallons on a gas pump? + How accurate & precise is the matching of the prior fuel level?
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On Thursday, July 20, 2017 at 9:42:15 AM UTC-4, Steve W. wrote:

Of course vehicle position and shut off point makes a difference. If you fill it up in a situation that winds up with more gas in it, then fill it up after your run in a situation that winds up with less gas in the tank, you think you used less gas than you actually did and you get slightly higher MPG.
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wrote:

No, steve. You are wrong. The amount of fuel you put in is the amount you can squeeze into the empty portion of the tank. The amount you used is the amount that used to be in the tank. You need to fill it to the exact same point each time to get an accurate reading. You may have filled your 72 liter tank to only 71 liters the last time you put in 50 liters to fill the tank. Now, at a different station, with different levels, you may squeeze in 73, or only 68. COSISTANCY is the key - and where most will fall down, because, like you, they just don't REALLY understand.
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On 7/20/2017 5:15 PM, snipped-for-privacy@snyder.on.ca wrote:

You buy gas by the gallon and mileage is miles per gallon. Summer gas has higher density so you get more gas by weight for your money but it costs more per gallon in the summer. Sounds like you can't win.
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Mad Roger wrote:

IF the odometer is accurate and you do the math out to the 10ths of a gallon the pump shows it can be VERY accurate.
--
Steve W.

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On Thu, 20 Jul 2017 12:08:33 -0000 (UTC), Mad Roger

This thread reminded me to run-the-numbers from my car's log book. I record each fill-up and a few times a year I'll plug the numbers into a home-made spreadsheet. I'm not sure if my car even has a built-in calculator - I'll have to check .. my brother's Buick will always show about 1 mpg better than reality.
in liters per 100 km my last 10 fill-ups are : 6.5 8.0 7.3 7.9 7.0 7.4 7.4 7.4 7.3 7.4 avg = 7.36 The adjacent high/low values indicate that the fill-up was filled-to-the-brim or not-quite-full due to the pump sensivity.
Interesting to compare winter driving with winter tires : 8.3 8.7 8.2 7.9 7.7 8.0 8.5 8.3 8.0 8.0 avg = 8.16
2015 Kia Rondo 6 speed auto ; 2 liter gas ; rated 10.6 / 7.6 city/highway at Natural Resources Canada http://oee.nrcan.gc.ca/fcr-rcf/public/index-e.cfm
John T.
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On Thu, 20 Jul 2017 11:58:39 -0400, snipped-for-privacy@ccanoemail.ca wrote:

That is a combination of snow tires, sloppy roads and cold weather - not just tires
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On Thu, 20 Jul 2017 17:22:06 -0400, snipped-for-privacy@snyder.on.ca wrote:

Yep - warming up in the driveway while I scrape the windows .. also I'll run the winter tires just a pound or two soft. John T.
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On Thu, 20 Jul 2017 18:08:32 -0400, snipped-for-privacy@ccanoemail.ca wrote:

and the engine runs richer with low intake air temps too. Amd the bearings and gears are stiffer in the cold, and you are pushing slush aside or crawling over snow - all of which takes more power and fuel.
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On 07/20/2017 03:22 PM, snipped-for-privacy@snyder.on.ca wrote:

And if you're like me, the car idling in the driveway until the ice melts off the windows and the interior temperature is somewhere north of zero (F).
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Trip meter miles depends on circumference of driving wheels. I know my speedo closely matches readings of roadside radar displays or my GPS, so I guess trip meter miles will be accurate too.
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On Thu, 20 Jul 2017 17:32:39 +0100, Mike Coon wrote:

Every reading a mom and pop does has inaccuracies that, I posit, are tremendously higher than most people seem to think they are (at least most people who quote mpg figures with decimal places in them).
Most people have a tripmeter reading and a gas pumpmeter reading. Where they fill the tank and reset the tripmeter before driving away.
I can't find any reliable source that says what the accuracy or repeatability of that mom-and-pop tripmeter/pumpmeter calculation, but basic logic dictates that the errors compound such that there is likely (IMHO) no way to get anywhere near decimal-point accuracy, and worse, probably plus or minus 1 mpg is the closest anyone can get in terms of repeatability and precision.
Even the EPA's $360,000 machine only claims plus or minus 2% of the indicared reading. I can't find where I got the notion that a mom and pop can't possibly get closer than about 4% with a tripmeter/pumpmeter mpg calculation - but I'm still seeking those numbers as we speak.
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On 07/21/2017 11:51 AM, Mad Roger wrote: ...

...
Why do errors compound in your view?
And, it depends on what you mean in terms of accuracy -- in terms of absolute one needs to know the calibration error of the odometer; most folks are satisfied to just assume it's close enough for the purpose.
If you look at simply a single fillup, it's not unreasonable to expect a few tenths of a gallon difference between the first fillup level and the subsequent; if you try it on shorter distances than a full tank then the fractional error goes up.
OTOH, if one keeps track over longer periods of multiple fillups and take some care to use the same filling pattern and only fills up after using near the full tank capacity, then over time plus/minus targets _will_ tend to cancel out and I have no qualms in believing a relative performance number in the 0.1 mpg can be determined.
As noted, I've done this on long trips a number of times (generally on first trip or so with a new vehicle, either actually new (rare) or (most often) new to me) just to see how it compared with previous and have had quite good comparisons on recent ones with the computer-computed results. These would be over total distances of 1500 to 2000 miles, not just 20 miles test runs.
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On Fri, 21 Jul 2017 12:42:08 -0500, dpb wrote:

It's like a chain is no stronger than the weakest link.
No calculated result can be better than the worse inaccuracy.

Accuracy, precision, and sigfigs are standard terms: http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html Accuracy: how closely a measured value agrees with the correct value. Precision: how closely individual measurements agree with each other. Sigfigs: accuracy is no better than the least accurate measurement.
By way of off-the-cuff example, if the accuracy of the odometer is to the billionth of a mile and the accuracy of the pump gallons is to the billionth of a gallon, but the accuracy of the fillup is plus or minus one gallon, then the resulting mathematical (division or multiplication) accuracy can be no better than plus or minus one gallon.

A single fillup will never suffice.
We're trying to compare a MPG *change* between two situations, so, by definition, there _must_ be (at the very least!) /two/ separate calculations. + Calculation before the change (say, smaller tire/wheel diameter) + Calculation after the change (say, larger time/wheel diameter)

That's not necessarily true, because it depends on the understimations balancing out the overestimations, but I'm not going to quibble that more calculations done over time are likely going to randomize the precision and accuracy fluctuations over time.
While I will not quibble with your statement (because I essentially agree with you), I can point out that your speedometer can be consistently wrong in the same direction in either precision or accuracy, in which case it's *not* going to balance out over time. It will be consistently wrong, over time.
But, let's not quibble about that because we both can assume that, for our purposes, the randomization of measurement results will be half the time underestimating and the other half the time overestimating - such that they could balance out.

Nobody yet, and even not me, has supported a claim for any better accuracy than my presumed plus or minus one mile per gallon using the standard mom-and-pop test of dividing the number of miles driven based on the tripmeter reading by the pump indication of gallons used to fill back up to a presumed similar previous starting point of amount of fuel consumed.
Remember, the resulting accuracy can't possibly be better than the least accurate measurement.
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On 07/21/2017 2:05 PM, Mad Roger wrote: ...

On a _point_ estimate, yes.
The point I'm making is that it is the _total_ fuel consumed over the total distance; the changes in hitting the target level on a tank-by-tank basis goes away for all excepting the last tank as it doesn't matter in the total. So, if you miss by 0.1 gal on the one tank, yeah, that roughly will translate to 0.1 on the mpg number. But, over the 9 tanks prior to the tenth and last, it doesn't matter; it was all used and so the 0.1 gal error on the last is only a tenth of the size on the overall as it was on the first.
So, over a time, you can get quite precise estimates this way.
As noted, the bias in odometer calibration is a bias, yes, but presuming there's not a reason it is getting worse with time it's not compounding, it just makes a percentage difference in the computed result.
--


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On Fri, 21 Jul 2017 14:20:43 -0500, dpb wrote:

Your multiple-runs argument only holds water for both random accuracy and random precision, but not if one is random and the other is not.
For example, I think it's well known that most speedometers read high *most* of the time (at least that's my understanding - but I could look that up if you question that assertion).
Assuming that assertion is close to correct, let's say they read high by about 5% accuracy most the time (just to make a point), where the precision is about plus or minus 1%.
Notice the accuracy is *always* high while the precision is random around a set point.
http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html Accuracy: how closely a measured value agrees with the correct value. Precision: how closely individual measurements agree with each other.
If the speedo reads high by 5% all the time, whether you measure your speed once or if you measure your speed a billion times, you'll never any closer to the right speed than 5% plus or minus 1%.
In repeatability, the gauge may give you different figures within + or - 1% of that 5%, which is only to say that the speed will be consistently reading from 4% to 6% higher than the actual speed.
But a billion test runs won't get you any better than that, all of which are at least 4% off from the "correct" measurement (in the example).
My point is that a billion test runs only randomizes that which is random.
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On 07/21/2017 5:05 PM, Mad Roger wrote: ...

We'd already thrown the mileage calibration bias out as being simply that. It can be compensated for by comparison over set measured course and recording the offset. Red herring for the discussion.
The point I'm making is that it doesn't matter at all about whether there's any random error in the fillup on individual tanks at all on the intermediary answers--yes, they may have some fluctuation owing to inconsistent fillup, but one can assume the pump is accurate since they're checked by the State weights and measures folks on a regular basis. So, all the fuel that went in went out in accumulating the miles and it didn't matter how much went in on each individual measurement at all in the end--it's the total. Only that random error on the final fillup when you make the calculation at the end does that error enter in -- and it becomes quite small by then in comparison to the total.
And, if one computes the mean of the billion trials, the error in the mean is quite small even if the random error in each trial is sizable.
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On Fri, 21 Jul 2017 18:05:52 -0500, dpb wrote:

I agree with you that the tripmeter calculation is inaccurate to some degree, for which there are ways of "calibrating" the equipment.

The answer to the question depends on only 3 factors, I think.
Given these three factors are critical to answer the question, I think everyone is talking out of their ass (including me) if they can't answer these three questions to validate their own thought process:
+ How accurate & precise is a reading of 300 miles on a your tripmeter? + How accurate & precise is a reading of 20.25 gallons on the gas pump? + How accurate & precise is the matching of the prior fuel level?
I posit both the tripmeter and the previous-fill-level measurements suck. How much to they suck?
I don't know.
I would not be surprised if they suck so badly that the end result is a calculation which is plus or minus 1 mile per gallon in either accuracy or repeatability.

While it will be useful to know what the accuracy and precision (repeatability) of the pump is, I think we can all assume that the pump is within something like (at least) plus or minus a few percent of what it reads.
But that number can be accurate to a billionth of a gallon, and it still would be meaningless if the fill level was off by plus or minus a gallon because the accuracy of any one measurement is only as good as the worst measurement and the accuracy of the final calculation (when multiplication adn division are involved) compounds inaccuracies.
Anyway, all the words are moot if we don't know the answer to 3 questions: + How accurate & precise is a reading of 300 miles on a your tripmeter? + How accurate & precise is a reading of 20.25 gallons on the gas pump? + How accurate & precise is the matching of the prior fuel level?

Am I correct to understand that you are saying if you go only 300 miles on one tank, then the fill-level inaccuracy is (say) plus or minus 1 gallon per tank; but if you go 3,000 miles (obviously on multiple tanks), that the fill-level inaccuracy is one tenth of that plus or minus one gallon per tank?

As long as the error is random (i.e., in both directions of the true answer).
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On Friday, July 21, 2017 at 7:30:35 PM UTC-4, Mad Roger wrote:

No, he's been saying the same thing for many posts now. If you fill up the tank 10 times, any inaccuracy from not exactly filling the tank to the same level at the first time and last time is reduced by an order of magnitude, because it only matters on the last fill. All the other 9 fills, you have the gas pump reading.
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