Calculate the spreading of points

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I have a set of points where a point is characterized by a pair of number $p_i = (x_i,y_i)$. The points are distributed in a specific area (say a rectangle). Is there a metric that characterizes the spreading of the points? Please have a look at the attached figures to see better what I'm trying to achieve. enter image description here Points in the left figures have the spreading degree smaller than the right. I'm thinking about the sum of Euclidean distances, but it will depend on the number of points.