[gone-ot]

Mathematical Delusion - The MPG variations are due to the "Law of Large Numbers."

Initially, right after filling up, the MILES and GALS numbers are both small and little changes are immediately seen on their result, ie: MPG = MILES / GALS

...for example, small initial changes:

MPG = (10/0.3) = 33.3 mpg ...BASELINE, 10 miles & 0.3 gallons.

MPG = (10/0.2) = 50.0 mpg ...-0.1 gal gas
MPG = (10/0.4) = 25.0 mpg ...+0.1 gal gas

MPG = ( 9/0.3) = 30.0 mpg ...-1 mile
MPG = (11/0.3) = 36.7 mpg ...+1 mile

...which are variations of +50%/-25% for gas and ±10% for mileage.

However, as you accumulate mileage, the MILES number becomes large enough to 'swamp' similar changes in the GAL number.

...for example, here are the same changes as above, except at a distance of 150 miles (same ×15 ratio):

MPG = (150/4.5) = 33.3 mpg ...BASELINE, 150 miles & 4.5 gallons.

MPG = (150/4.4) = 34.1 mpg ...-0.1 gal gas
MPG = (150/4.6) = 32.6 mpg ...+0.1 gal gas

MPG = (149/4.5) = 33.1 mpg ...-1 mile
MPG = (151/4.5) = 33.6 mpg ...+1 mile

...which are variations of just ±2% for gas and ±1% for mileage.

Thus, as the mileage and gas input numbers get larger the the resulting variations in the MPG numbers become smaller, even though the changes were identical!