To gain some geometric insights and clarification, we will start with a population of three values, "x"1, "x"2, "x"3. This defines a point "P" = ("x"1, "x"2, "x"3) in R3. Consider the line "L" = {("r", "r", "r") : "r" ∈ R}. This is the "main diagonal" going through the origin. If our three given values were all equal, then the standard deviation would be zero and "P" would lie on "L". So it is not unreasonable to assume that the standard deviation is related to the "distance" of "P" to "L". That is indeed the case. To move orthogonally from "L" to the point "P", one begins at the point: