In your circuit for this test A0 ahould be connected to the ADC ground at the chip, as in @TomGeorge reply #24
Can you edit your code so as to collect the sample readings into an array and print them out when all the readings have been taken?
Then we can eliminate the serial print as the source of the noise.
That is because the S_D coonversion process acts as a filter - as shown in the dasta sheet.