Question

Hi all this is a very simple question, but my mind is a bit empty and i can’t seem to find any satisfactory results on the internet.

Given a collection of 2d points (x,y), how can I determine how tightly grouped they are together.

Thanks

I guess an example would of helped.. I am trying to measure the “wobble” when aiming at a target, so I have every point the shooter aimed and I would like to see if they were steady or if they moved allot.

Answer 1

It depends on your definition of “tight grouping”. One possibility is the sample variance, or the corresponding standard deviation. Crudely speaking, this gives you an “average” distance away from the centre point (which can be defined either as a known point, or as simply the average of your dataset).

For a group of 2D points, this can be defined as:

stddev = sqrt(var) = sqrt(1/N * SUM { (x - x0)^2 + (y - y0)^2 })

where (x0,y0) is the sample mean (i.e. the average of all your points).

This metric will be less sensitive to outliers than e.g. the bounding box metric.