Odd Intersection Property
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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.
![](oddint4.gif)
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)
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- 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!
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![](oddint3.gif)
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- 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!
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