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Some papers from Analog Devices (like this one - page 2) and other sources indicates that the rms noise of a histogram plot of an ADC output can be found by calculating the standard deviation of the distribution. So, the standard deviation is in fact the rms noise.

sample

I'm trying to calculate the standard deviation using an online calculator (to speed up calc) for some histograms in the same application note but the values that I get are always wrong from the application note, so it's clear that I'm totally lost here.

Can anyone help me to calculate the rms noise of a given ADC histogram considering that I have the ADC values x number of ocurrences of each value?

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The standard deviation is calculated on the set of output codes recorded at the output of the ADC. If you have the data in time sequence as is was captured, you can calculate the standard deviation directly from that data set. If the data has already been converted to histogram form, as you describe above, you will need to enter each output code value into your data set as many times as the counts that are in its histogram bin.

For example, if code 127 had 3 hits, code 128 had 7 hits, and code 129 had 4 hits, you would enter this into the online calculator:

127, 127, 127, 128, 128, 128, 128, 128, 128, 128, 129, 129, 129, 129

(your data set should be much larger of course)

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