I would suggest asking the electric utility to either test or replace the meter.

Beyond that, it may be necessary to (have someone) perform some tests to determine if there is some appliance is using excessive amounts of electricity.

How are the major appliances (Range, heat, water heater, clothes dryer) powered? Electricity, natural gas, propane, or oil?

Does anyone in the house take extraordinarily long showers (longer than 10 minutes)?