My calculated mpg has been between 0 and 6 mpg different (worse) than the displayed average mpg. That is as close as could be expected really. Most people do not keep logs so most manufacturers err on the optimistic side to keep customers happy. They hear a lot of complaints if they erred on the pessimistically.
If you think about the complex variables that go into a displayed estimation, it is amazing that they get it so close. Start with one "real" number, the minuscule amounts of gas per injection that are added up to billions of times over one fill up and integrated with the rest of the data. Add driving style, temperature, wind conditions, elevation changes, traffic conditions, and even if you top off your tank (I do) versus the really random "first" click.
In any case, if you are doing calculated fill up mpg, you now have a decent adjustment for the displayed mpg. You can do something similar with the displayed mph, and the odometer. You didn't think those were accurate either did you?
Most fill ups, my displayed and calculated mpg were like yours, 3 mpg different. So I use that as my expected mpg. I've already learned how to impact the results in driving style the last couple hundred miles of the tank, so I have a number of adjustments I use to predict final calculated number before I actually fill up.
Go full OCD, or just stop sweating the small details!
2018 Kia LX HEV Metal Stream with Advanced Tech