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

enter image description here

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.

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

enter image description here

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.)

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

enter image description here

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.

Source Link
user334128
user334128

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:

enter image description here

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.)