Odd Intersection Property

What it is:
 The odd intersection property states that the two
median levels, of any two given points sets will cross an odd number
of times. We can see this by drawing a diagram below (they
cross 3 times).
 Or, we can see it in the fact that if at one line is above another, then they will have to cross an odd number
of times for it to be below.
As, we can see from the diagram the two median levels (denoted
by the darker red and blue lines) cross an odd number of times.
(denoted by the green dots)


 This means that if we take any interval over the
entire diagram, then the odd intersection property holds if the
median levels flip positions in that interval!



 Let's take a look at an example:
 Let x1 = 5, and x2 = 12
 Let the red median levels be equal to: L1(5) =
7, and L1(12) = 13
 Let the blue medians be equal to: L2(5) = 9,
and L2(12) = 5
L1(5)  L2(5) = 7  9 = 2
L1(12)  L2(12) = 13  5 = 7
 Using the formula we get:
2 * 7 = 14, which is less than 0.
So the odd intersection property holds for this
interval!
