Hello jimford
I use the Arduino with Pololu Current Hall sensors (Pololu 1186) for remote network current measurement.
I see your sensor has 5V operating voltage:
Try this:
be sure the sensor-arduino cables are as short as possible
connect the sensor Vcc to the Arduino Analog Reference pin (NOT to other 5V pins or external source!!)
connect the sensor OUT with a shielded cable (shield to GND)
try several GND Arduino pins for sensor GND pin connection to minimize the jitter, it should be the GND pin with physically shortest connection to the A/D converter IC
try to more stabilize the arduino main voltage, the usb connection only may not be sufficient
The digital A/D output ripple should be in WORST CASE not over +-1, for example 511,512,513
Hope this helps
Regards
Pavel