Is the following definition of the variance of the number of points correct? I have been asked to calculate "the variance of the number of points" in the following pictures, inside the circles:

I was looking for the definition of "the variance of the number of points" in the literature, which I found this one:
The variance of a set of points is the sum of the squares of the distances from each point to the centroid of the set.
Is this the correct definition of "the variance of the number of points"? (Intuitively, one also expects the division by the number of points, which is absent in this definition.)
EDIT
The pictures are taken from here. For example, it says the variance of the number of points in the left picture scales as $R^2$, but it doesn't give any definition of the variance of the number of points and how it is calculated.

Per Wikipedia on to quote:

Spatial variability occurs when a quantity that is measured at different spatial locations exhibits values that differ across the locations. Spatial variability can be assessed using spatial descriptive statistics...

In accord with the above, a sampling scheme that may assist is as follows:

*

*Draw a horizontal diameter (an x-axis) for each circle.


*Fit a simple linear (two-parameter) regression model (Least-Squares or perhaps a robust Least-Absolute Deviations model) to predict the x-values (dependent variable) versus the # of the point in the sample (independent variable) as they occur and happen to fall on the diameter.


*Select one of the usual goodness-of-fit metrics for the regression model.


*Rank the circles based on the chosen comparative statistic.
Arguably, a valid spatial variability analysis concurrent with the definition provided above, as to quote, "a quantity that is measured at different spatial locations exhibits values that differ across the locations". Note, clearly an extension from the recommended mean model (which recommended the employment of the distance formula) as compared to a linear model. Likely, in my opinion, more informative than a mean model and executed with a sampling design that is a de facto data-reduction technique (often necessary).
