I need to know how precise a measurement system is, expressed as a standard deviation. I don't really have much of a background in math so please excuse me if I'm a bit unclear or inaccurate about something.

The simplest way I know of doing this is by taking e.g. 100 measurements of the same object and then using the usual sample standard deviation formula.

Unfortunately, I can't use this method. I must measure different objects multiple times. Let's say 10 objects, 10 times each.

The thing that comes to mind is to calculate the mean for each group, subtract the relevant means from each measurement (sort of a normalisation) and then calculate the standard deviation from the resulting 100 numbers. Does this make sense? If not, how do I approach the problem?

The simplest way I know of doing this is by taking e.g. 100 measurements of the same object and then using the usual sample standard deviation formula.

Unfortunately, I can't use this method. I must measure different objects multiple times. Let's say 10 objects, 10 times each.

The thing that comes to mind is to calculate the mean for each group, subtract the relevant means from each measurement (sort of a normalisation) and then calculate the standard deviation from the resulting 100 numbers. Does this make sense? If not, how do I approach the problem?