I don't know the proper term for "spreaded" but what I want to find is, a value that indicates how far is an average point from the centroid.
I think this is standard deviation of the point set, but I need metrics.
For instance, consider the figures:
Here, blue points are centroids and black points are the points in the cloud.
In both cases, standard deviation is the same, but the first cloud is more "spreaded".
If a spread factor $\alpha$ were to be given, how would you compute $\alpha$ given the 3D coordinates of the points?
I don't understand your gripe with standard deviation. However, here's something that should work:
Let $\{(x_i,y_i,z_i): i = 1,\dots n\}$ be a collection of points. Let $(x,y,z) = \frac 1n \sum_{i=1}^n (x_i,y_i,z_i)$ be the centroid. We can take $$ \sigma^2 = \frac{\sum_{i=1}^n ((x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2)}{n} $$ $\sigma = \sqrt{\sigma^2}$ gives you the standard deviation in Euclidean distance of all points from the centroid, which should be exactly what you're looking for.