How to calculate r.m.s radius of a N-body system?

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To calculate the root mean square (r.m.s) radius of a globular cluster, one can use two methods: measuring a set of points or mapping the waveform. The first method's accuracy depends on the number of points measured, while the second method is more precise but poses challenges in data collection. The r.m.s radius reflects the average deviation of the cluster's radius from that of a circle with the same area. Calculating this may involve advanced calculus techniques. Further insights or solutions on this topic would be appreciated.
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an example of a globular clusters, what method should be used to calculate the root mean square radius of it? thanks in advance!
 
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I don't know how you would collect the data for something like that, but if you did the formula's are here:

http://en.wikipedia.org/wiki/Root_mean_square

The first one would be if you took a bunch of points, the second if you map the waveform. The first one would not be too accurate, or only as accurate as the amount of points you decide to measure I should say. The second one would be accurate but I really don't know how you would collect that data. Remember you are looking for the average of how much the radius of your cluster deviates from the radius of a circle of the same area. Sounds like mega-calculus to me, if you find an answer I'd be interested to see what it is.
 

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