How to Detect voltage Noise in the analog pins.

I'm using the analog pin (A0) to control a relay using a power supply and a battery. The reading is perfect until I remove the battery. I get noise and numbers are all over the place.

I want to know what code can I write to detect that the reading has gone berserk so I can notify myself?

Here is the reading below coming out of the serial monitor 498 410 355 969 1023 1023 897 539 438 373 980 1023 1023 719 500 411 356 986 1023 1023 792 516 422 363 967 1023 1023 712 500 409 355

Compute the difference between the current reading and the last reading. If it is ten times greater than anything you'd normally see in your software, then assume that the battery was disconnected. You could possible install a 100k pulldown down resistor to ground on the analog pin, and then readings would just drop to zero when the battery is disconnected. 100k shouldn't interfere with the pin's ability to drive the pin high on a digitalWrite().

Can you post a picture of your schema?