The average person doesn't exist

Assuming Normal distribution (or close enough), the “average person” is the Maximum likelihood point estimate. Although the probability may be the biggest at the “average person” across the whole space, it is still impossible to find the average person if we consider the average of many variables.

Assume a spherical Gaussian distribution defined in a high-dimensional space. As we increase the dimension, the probability mass in a unit ball centered at the origin yields almost zero probability mass. The volume near the origin is just too small in a high-dimensional space. See Gaussian annulus theorem from Foundations of Data Science. High dimensional space is counterintuitive.


Humble Pi < > High dimensional space is counterintuitive