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**'Distance' between MANY points ??**

It's easy to calculate the Euclidean distance between two points A and B.

Between 3 points we can do the Eucliean distance between AB, AC and BC, and then take the average of the three to find the "distance" (I don't know what it's called for more than 2 points!).

But I have 8900 points, and to go about finding "how similar" the points are, in this manner, would take (8900 choose 2) = 39600550 calculations of the euclidean distance (not practical!)

Is there a good way to find the 'similarity' between a large number of points ??

One way I considered was, finding the median (centre of mass) of the object whose boundary was formed by connecting the 8900 points, and then determining what the Euclidean distance is between this 'median' and the FARTHEST point (out of the 8900) from that median.

This is not good if my 8900 points form a shape like a tight ball with one small sharp spike sticking out.

Another method would maybe be finding the Euclidean distance between the median and all 8900 other points, and averaging this (8900 calculations is much less than 39600550).

But how is this problem usually addressed ?? Can anyone please tell me what they know, or refer me to some literature ?? Thanks!!!