On a PCB of a irrelevant project I tested the simple ADCin and display the result on the LCD.

As Richard says the +/-1 LSB is what I get with no process. Occasionaly 2 LSBs.

I just sample every sec. and display it.

Of course the PCB is double sided with lot of ground, a cap on the ADC input pin and linear 5Volt regulator. So any external noise is minimized.

Breadboards are just a noise antennas and never give clean results.

Ioannis