Assume I have a dataset lies within a ball centered around the origin, I want to test the uniformity of the point distributed in the ball. In addition, I have all the distances to the origin computed as a side-product from previous step. I am not familiar with statistical test, what are natural choices of tests can I try?
A naive test I can think of is to compute the mean compare it with the origin, the farther the mean is deviated from the origin, the more skewed the dataset is.
Or, I can compute the skew, but this doesn't take advantage of the distances I already have.
I know this may depend on how accurate and solid I need it to be, I need a quick test that doesn't have to be very tight, but I'd like to have it based on well-known theory.
Thanks