# average difference between two sets of values

I've been keeping track of my car's gas mileage by calculating gallons divided by miles traveled miles traveled divided by gallons. The car itself calculates this mileage as well, but its values are always a little higher than the calculated values.

I was just wondering about the best way to calculate, I guess, the average or typical amount that the car's numbers are different from mine. My understanding of statistics is pretty much nil, so I was hoping somebody could point me in the right direction.

• It really depends on what you need to do with it, what properties you want it to have, but something like a mean absolute deviation, or a root-mean-square-error might serve your purpose. – Glen_b Sep 30 '14 at 23:45
• Usually, someone would calculate miles traveled divided by gallons consumed. This gives you mpg. You are calculating gallons per mile, which may be of interest, but is certainly less common. Also, since you are certainly using the same mileage number the car is (ie from the odometer), the difference must be in the car's inaccurate measure of gallons consumed; you may want to track those numbers more directly. – gung Oct 1 '14 at 0:18
• A seemingly simple solution based on the available information provided is to take the difference between your calculation and the car's calculation during randomly selected fill-ups throughout the year and then taking a simple average of the differences during the year. You should pay careful attention to minimize variability between measurements by ensuring you always use the same type of gas, same amount of gas, and have the same number of passengers with the same weight, and travel the same roads. If you can't, these differences will come out in as measurement error in your calculation. – StatsStudent Feb 18 '15 at 17:21