2010 Fuel Gauge problem

I posted this on the Mercury group but I don't see any activity. The Grand Marquis is very close to the Crown Vic so I hope someone can help.
My 2010 Grand Marquis has developed a problem with its fuel gauge.
Last week I filled the tank but the gauge stayed at 1/4. On the way home it increased slightly. When I drove as few days later it went up to about 1/2. Again, the next time I drove it increased to about 3/4. Now, about a week later it is indicating full.
Any Ideas as to the cause?
Thanks,
Bill A
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Maybe the fuel tank level sensing arm?? <http://www.partstrain.com/store/details/Replacement/Fuel_Sending_Unit/ARBF670303.html
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unit. The late model Ford fuel sender is 16 ohms when empty, and 158 ohms when full. This means that if the connections get corrosion on them and partially short, the guage will read LOW. Different than the older Fords where empty was about 90 ohms and full was 10, so an open read empty and a short read full. The late model Fords will read FULL when disconnected, and empty when shorted to ground. If the connector has "the greenies" it will read low when wet.
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This may or may not ease your mind. I had a 2005 crown vic and for no apparent reason the fuel gauge did not read correctly one day. Didn't read correctly again till I filled the tank up after driving several hundred miles. The thing is all computer controlled, even though the sender might still be the old fashioned float. I think it got confused for whatever reason and didn't reset till the tank was refilled again. So don't do anything until you've driven it a hundred miles or so and filled it up one more time.
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