I agree with the others who say 1/2 tank is just too short and too inaccurate.
One thing I was doing was filling to the nearest $0.25. Oddly, when gas went up in price, it "seemed" my fuel economy went down.
Why?
Well, stopping at the nearest $0.25 often put less "extra" gas in the tank from where the pump stopped. If gas costs more, I get less.
So what did I do? I changed my metric to the nearest $0.50 and it "seems" that I get better mileage.
Of course, the long term number is the one that matters, and my 1994 Geo Prizm over the past 86K+ miles has averaged 31.8 MPG from 106K miles to 192K miles on the odometer.
One other thing, when I went from 175/65R14's to 185/65R14's my MPG dropped. Why? Because the odometer recorded fewer miles to go the same distance.