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You are right, we are doing an average of averages. By doing it this way we get a more accurate representation of what the actual mileage may be.
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Well, I'd say you get a better idea of what your expected range of milages could be, but your actual average is your actual average, and doing an average of averages won't give you that.
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We also get an idea of what the high & low mpg's will be. Using Statistical Analysis will allow us to monitor trends in the mileage of the car over it's lifetime.
For instance, if we discover a lowering of mpg over a period of time we know that something has changed. Whether or not it is the type/grade/quality of fuel we are using, the season we are driving in, heavier traffic, or perhaps a problem with the car.
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This is very true, and I think is the main advantage to using your method. Another way to do this is to track moving averages to smooth out any bumps in individual fillups, and let you see long term trends more easily. I use this here in Minnesota to track the effects of seasonal temperature changes, as we have a really wide range here ( about -25 to 100 F)
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Also the more observations (fill ups) you have, the closer it will come to your Total Miles/Total Gallons used method.
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Agree 100% on this one.