I can't really speak about 328i average mpg, but here are a few things to check that can make it better in general.
1. Tire pressure. Driving on under inflated tires can cause bad mpg.
2. Your right foot. Stomping on the accelerator will dramatically drop your mpg.
3. Fuel grade. If you can, try some ethanol-free 93 octane gas.
4. Maintenance. Make sure you change your fluids and filters on time.
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